C.H. Papadimitriou. On selecting a satisfying truth assignment. FOCS, pages 163--169, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... Perhaps one can perform a more detailed analysis of the Markov chains for some such random walk algorithm, without collapsing assignments with the same Hamming distance from some target assignment, together into one state as is done here and in the analysis of a 2 SAT algorithm given in [20]. It may also be of interest to attempt to prove time lower bounds on restricted classes of random walk algorithms. For instance, the algorithm in this paper picks a variable to ip based only on the number of clauses that would be lost by ipping each variable (that is, the quantity jL(A; v)j ....

C. H. Papadimitriou. On selecting a satisfying truth assignment (Extended Abstract) . 32nd IEEE Symposium on Foundations of Comput. Sci., 1991, pp. 163-169.

....other clauses. We repeat this procedure, until hopefully all clauses are satis ed. Since the CNF may be unsatis able, we usually put a time limit on the number of iterations, and once the limit has been reached, we give up. The simplest variant of this local approach, originally introduced by [23], is at the center of our current investigation. This algorithm, denoted RWalkSAT, relies on randomness in all its decisions. Thus, the initial assignment is picked at random, at each step a random unsatis ed clause is picked, and this clause is corrected by ipping a random literal in the ....

....RWalkSAT, relies on randomness in all its decisions. Thus, the initial assignment is picked at random, at each step a random unsatis ed clause is picked, and this clause is corrected by ipping a random literal in the clause. Surprisingly, RWalkSAT behaves much better than one might expect. [23] proved that it succeeds in nding a satisfying assignment in expected quadratic time on any satis able 2 CNF. Although 2SAT is solvable in polynomial time, it is not obvious that such a simple local heuristic as RWalkSAT is good enough to solve it. Another interesting result is that on any ....

Papadimitriou, C. H. On selecting a satisfying truth assignment. In Proceedings of the 32nd Annual IEEE FOCS'91, pages 163-169,

....algorithm for MAX k SAT whose worst case time bound depends on the number of variables. Our algorithm and its analysis are based on Sch oning s proof of the best current worst case time bound for k SAT [40] Similarly to Sch oning s algorithm (which is also very close to Papadimitriou s algorithm [36] and the experimentally successful WalkSAT family by Selman et al. 41,31] our algorithm makes random walks of polynomial length. We prove that the probability of error in each walk is at most 1 c k; where N is the number of variables, and c k; 2 is a constant depending on k and . ....

....experimentally (see [4,18,27] for surveys on the subject) Both complete and incomplete algorithms are studied in this eld. The incomplete algorithms mainly use local search (see, e.g. 14,15,19,25,29,39,41] Theoretical study of worst case upper bounds for such algorithms was very limited [24,36]. Recently, Sch oning [40] proved the upper bound (2 2=k) on the worst case running time of a randomized local search algorithm for k SAT. The algorithm he used is close to Papadimitriou s 2 SAT algorithm [36] this random walk procedure is also an important component of some of the empirically ....

[Article contains additional citation context not shown here]

C. H. Papadimitriou. On selecting a satisfying truth assignment. In Proceedings of the 32nd Annual IEEE Symposium on Foundations of Computer Science, FOCS'91, pages 163-169, 1991.

....therefore, throughout this paper we will speak only about satis able formulas. Most incomplete heuristic algorithms use local search paradigm (this line of research started from experiments of Gu [8] and Selman, Levesque and Mitchell [34] and theoretical work by Koutsoupias and Papadimitriou [19, 26]) Such an algorithm chooses a random initial assignment and then modi es it step by step until it nds a satisfying assignment. If the random walk is long enough, it is restarted from another initial assignment. There is a number of experimentally studied SAT local search algorithms, for ....

Papadimitriou, C. H.: 1991, `On selecting a satisfying truth assignment'. In: Proceedings of the 32nd Annual IEEE Symposium on Foundations of Computer Science, FOCS'91. pp. 163-169.

....RIGHT or LEFT. The result of the Hadamard transformation is shown in (b) the particle is now in an equal superposition of LEFT and RIGHT chirality states (with the amplitudes indicated) and then moves accordingly (c) to generate the state at time t l. gorithm similar to that of Papadimitriou [27] that gives a the most efficient known solution to 3SAT. In general, Markov chain simulation has emerged as a powerful algorithmic tool and has had a profound impact on random sampling and approximate counting [18] Among its numerous applications are estimating the volume of convex bodies [10] ....

C. Papadimitriou. On selecting a satisfying truth assignment. In Proceedings of the 32nd Annual Symposium on Foundations of Computer Science, pages 163-169, San Juan, Puerto Rico, 1-4 October 1991. IEEE Computer Society.

....throughout this paper we will speak only about satis able formulas. Most incomplete heuristic algorithms use local search paradigm (this line of research started from experiments of Gu [Gu92] and Selman, Levesque and Mitchell [SLM92] and theoretical work by Koutsoupias and Papadimitriou [KP92,Pap91]) Such an algorithm chooses a random initial assignment and then modi es it step by step until it nds a satisfying assignment. If the random walk is long enough, it is restarted from another initial assignment. There is a number of experimentally studied SAT local search algorithms, for ....

C. H. Papadimitriou. On selecting a satisfying truth assignment. In Proceedings of the 32nd Annual IEEE Symposium on Foundations of Computer Science, FOCS'91, pages 163-169, 1991.

....assignment The algorithm terminates. 4. Pick a clause from . Take C as the value of g(p ) Generate Nbhd(p ,C) Boundary=Boundary (Nbhd(p ,C) Body) Body = Body p . 5. Go to step 2. Interestingly, the described algorithm can be viewed as an extension of Papadimitriou s algorithm [10] and Walksat [12] to the case of unsatisfiable CNF formulas. Papadimitriou s algorithm and Walksat can be applied only to satisfiable CNF formulas since they do not store visited points of the Boolean space. The remarkable fact is that the number of points that one has to explore to prove the ....

C.Papadimitriou. On selecting a satisfying truth assignment. Proceedings of FOC-91.

....all these bounds for deterministic algorithms. Probabilistic Algorithm. Our algorithm is inspired by the currently fastest probabilistic 3 SAT algorithm of [15] which uses a well known heuristic search method, cf. 2, 9] This algorithm is based on random walks (like Papadimitriou s algorithm [11] for 2 SAT) Given a formula F in k CNF with n variables, the algorithm chooses exponentially many initial assignments at random and runs local search for each of them. Namely, if the assignment does not satisfy F , then the algorithm chooses any unsatis ed clause, chooses a literal from this ....

C. H. Papadimitriou. On selecting a satisfying truth assignment. In Proceedings of the 32nd Annual IEEE Symposium on Foundations of Computer Science, FOCS'91, pages 163-169, 1991.

....throughout this paper we will speak only about satis able formulas. Most incomplete heuristic algorithms use local search paradigm (this line of research started from experiments of Gu [Gu92] and Selman, Levesque and Mitchell [SLM92] and theoretical work by Koutsoupias and Papadimitriou [KP92, Pap91] Such an algorithm chooses a random initial assignment and then modi es it step by step until it nds a satisfying assignment. If the random walk is long enough, it is restarted from another initial assignment. There is a number of experimentally studied SAT local search algorithms, for ....

....[PPZ97, PPSZ98] 4. It is known [SSW01] that changing the distribution of initial assignment (from a uniform distribution to a di erent one) results in improved worst case upper bounds on the running time of a local search algorithm. Also it is easy to see that Papadimitriou s algorithm for 2 CNF [Pap91] can choose initial assignment from the set of only two assignments (all True and all False) without worsening its worst case running time. On the other hand, it is shown in [DHIV01] that one can choose a random permutation from a set of naturally constructed O(n 3 ) permutations without ....

C. H. Papadimitriou. On selecting a satisfying truth assignment. In Proceedings of the 32nd Annual IEEE Symposium on Foundations of Computer Science, FOCS'91, pages 163-169, 1991.

....right or left. The result of the Hadamard transformation is shown in (b) the particle is now in an equal superposition of left and right chirality states (with the amplitudes indicated) and then moves accordingly (c) to generate the state at time t 1. gorithm similar to that of Papadimitriou [27] that gives a the most ecient known solution to 3SAT. In general, Markov chain simulation has emerged as a powerful algorithmic tool and has had a profound impact on random sampling and approximate counting [18] Among its numerous applications are estimating the volume of convex bodies [10] see ....

C. Papadimitriou. On selecting a satisfying truth assignment. In Proceedings of the 32nd Annual Symposium on Foundations of Computer Science, pages 163-169, San Juan, Puerto Rico, 1-4 October 1991. IEEE Computer Society.

....on the distributed solver to correspond to needing an e#cient parallel solution, such as one in NC k . For the solver we study a parallel version of the iterative repair procedure Wsat [ Selman et al. 1996 ] also known as walksat, as it uses a random walk over the unsatisfied clauses [ Papadimitriou, 1991 ] Firstly, in Section 2, we consider the scaling of the standard sequential Wsat, and find it is basically linear, O(n) at least for # # 3.8. In Section 3, we study a direct parallelization, and find empirically that is is exponentially faster, O(log(n) 2 ) up to # # 3.8 and possibly ....

C.H. Papadimitriou. On selecting a satisfying truth assignment. In Proc. IEEE symposium on Foundations of Computer Science, pages 163--169, 1991.

....that the size of instances which can be solved in practical time has been increased from some 30 50 variables ten years ago to even 10 5 variables recently. One drawback of this approach is, however, that it is very hard to prove its performance. Excepting for a very few theoretical analyses [20, 16, 23], most authors claim the performance of their programs by experiments, which involve intrinsic difficulties like how to select benchmark instances. In this paper, we do not discuss this kind of unguaranteed speedups but we discuss a guaranteed speedup, or what we call, a speedup by implementation. ....

Papadimitriou, C.H., "On selecting a satisfying truth assignment," Proc. FOCS'91, pp.163--169, 1991.

....study of SAT and MAX SAT algorithms is also very extensive ( 9] is a survey) Both complete and incomplete algorithms are studied in this field, the incomplete algorithms mainly use local search or and random walk. Theoretical study of worst case upper bounds for such algorithms was very limited [14, 16, 19]. Recently, Schoning [21] presented a striking randomized local search algorithm for k SAT resembling Papadimitriou s polynomial time algorithm for 2 SAT [19] Schoning s algorithm runs in the time (2(k 1) k) N . This algorithm picks an initial assignment A at random and then performs a local ....

....mainly use local search or and random walk. Theoretical study of worst case upper bounds for such algorithms was very limited [14, 16, 19] Recently, Schoning [21] presented a striking randomized local search algorithm for k SAT resembling Papadimitriou s polynomial time algorithm for 2 SAT [19]. Schoning s algorithm runs in the time (2(k 1) k) N . This algorithm picks an initial assignment A at random and then performs a local search: at each step, it (deterministically 2 ) chooses a clause unsatisfied by the current assignment A, picks a variable from this clause at random, and ....

PAPADIMITRIOU, C. H. On selecting a satisfying truth assignment. In Proceedings of the 32nd Annual IEEE Symposium on Foundations of Computer Science, FOCS'91 (1991), pp. 163--169.

....ON RANDOM 2 p SAT In this section we present results of experimental tests of NOVELTY on the instance collections described in Section 2. 4. 1 0 p p 0 : Typical cost appears to be a low polynomial Some analytic results are known for this class of algorithm when p = 0 (2 SAT) Papadimitriou [16] showed that for a simple random walk algorithm also based on flipping variables in an unsatisfied clause, a run length of O(n 2 ) is sufficient to solve any 2 SAT instance with probability at least 1 2 . For p 0, Random 2 p SAT is NP complete since any 3 SAT instance may constitute the pm ....

C. H. Papadimitriou, `On selecting a satisfying truth assignment', in Proc. 32nd IEEE Symp. on the Foundations of Comp. Sci., pp. 163-- 169, (1991).

....if and only if no strongly connected component contains a variable and its negation. If the formula is satisfiable then a satisfying assignment can be easily constructed. If the formula is not satisfiable then this process does not seem to indicate how unsatisfied the formula is. Papadimitriou [Pap91] describes a beautiful randomized algorithm for testing the satisfiability of 2 SAT formulae based on random walks. Is this algorithm guaranteed to find almost satisfying assignments to almost satisfiable 2 SAT formula As far as we know, no one considered this question before. It does not seem to ....

C.H. Papadimitriou. On selecting a satisfying truth assignment (extended abstract). In Proceedings of the 32rd Annual IEEE Symposium on Foundations of Computer Science, San Juan, Puerto Rico, pages 163--169, 1991.

....proves the theorem. 2 Adding Random Walk GWSAT Next, we show that by adding random walk (Selman, Kautz, Cohen 1994) basic GSAT can be made PAC. This result extends earlier work which established that satisfiable 2 SAT instances are solved by pure random walk in O(n 2 ) time on average (Papadimitriou 1991). Using similar techniques, we first show that from an arbitrary assignment, the hamming distance to the nearest solution can always be decreased by a random walk step (flipping a variable in a randomly selected, currently unsatisfied clause) Lemma 1 Let a be the current (non solution) ....

Papadimitriou, C. 1991. On Selecting a Satisfying Truth Assignment. In Proc. 32nd IEEE Symposium on the Foundations of Computer Science, 163--169.

....feature of WSat is that, unlike earlier local search algorithms, it chooses an unsatisfied clause and then flips a variable appearing in that clause: Select variable from clause must return a variable mentioned in clause. This architecture was first seen in the random walk algorithm due to Papadimitriou (1991). WSat may use di#erent strategies for Selectvariable from clause. In this study, we used the SKC strategy introduced by Selman, Kautz and Cohen (1994) we refer to this combination simply as WSat. Pseudocode for the SKC strategy is given in Figure 2. We follow Hoos (1998) in our approach to ....

Papadimitriou, C. H. (1991). On selecting a satisfying truth assignment. In Proc. 32nd IEEE Symp. on the Foundations of Comp. Sci., pp. 163--169.

....feature of WSat is that, unlike earlier local search algorithms, it chooses an unsatisfied clause and then flips a variable appearing in that clause: Select variable from clause must return a variable mentioned in clause. This architecture was first seen in the random walk algorithm due to Papadimitriou (1991). WSat may use different strategies for Selectvariable from clause. In this study, we used the SKC strategy introduced by Selman, Kautz and Cohen (1994) we refer to this combination simply as WSat. Pseudocode for the SKC strategy is given in Figure 2. We follow Hoos (1998) in our approach to ....

Papadimitriou, C. H. (1991). On selecting a satisfying truth assignment. In Proc. 32nd IEEE Symp. on the Foundations of Comp. Sci., pp. 163--169.

....number of flips, max flips. The name wsat, or WalkSAT, arises because the selection of random clauses can be regarded as doing a random walk on the unsatisfied clauses. This simple algorithm works surprisingly well on 2SAT it will find a solution, if one exists, in (expected) quadratic time [50]. Of course, 2SAT is tractable, and for this to work well on general intractable SAT we need to include powerful heuristics. 3.3.2 Heuristics in Wsat The basic practical Wsat method [67] is illustrated in Figure 5, with supporting routines given in Figures 6, 7, and 8. proc WSAT for t : 1 to ....

C.H. Papadimitriou. On selecting a satisfying truth assignment. In Proc. IEEE symposium on Foundations of Computer Science, pages 163--169, 1991.

....ed literal with is necessarily correct. Lemma 2 For all C 2 C, for all T, there is some variable v such that either v s c 2 C or v u x 2 C. In particular, the latter case must hold for all C 2 C u . Proof: Tm must make every clause true. QED 2 This argument is similar to the one used in [4] to show that satis able 2 SAT instances are solved by pure random walk in O(n 2 ) time on average. 4 We notice that if a trap exists, then every T reachable from it is also a trap. Furthermore, it a trap exists then there must be some minimum value h 0 of h, where h 0 0, among all ....

C. Papadimitriou. On Selecting a Satisfying Truth Assignment. In Proc. 32nd IEEE Symposium on the Foundations of Computer Science, pages 163{ 169, 1991.

....study of SAT and MAX SAT algorithms is also very extensive ( 9] is a survey) Both complete and incomplete algorithms are studied in this eld, the incomplete algorithms mainly use local search or and random walk. Theoretical study of worst case upper bounds for such algorithms was very limited [14, 16, 19]. Recently, Sch oning [21] presented a striking randomized local search algorithm for k SAT resembling Papadimitriou s polynomial time algorithm for 2SAT [19] Sch oning s algorithm runs in the time (2(k 1) k) N . This algorithm picks an initial assignment A at random and then performs a local ....

....mainly use local search or and random walk. Theoretical study of worst case upper bounds for such algorithms was very limited [14, 16, 19] Recently, Sch oning [21] presented a striking randomized local search algorithm for k SAT resembling Papadimitriou s polynomial time algorithm for 2SAT [19]. Sch oning s algorithm runs in the time (2(k 1) k) N . This algorithm picks an initial assignment A at random and then performs a local search: at each step, it (deterministically 2 ) chooses a clause unsatis ed by the current assignment A, picks a variable from this clause at random, and ....

C. H. Papadimitriou. On selecting a satisfying truth assignment. In Proceedings of the 32nd Annual IEEE Symposium on Foundations of Computer Science, FOCS'91, pages 163-169, 1991.

....for large k. In this paper we improve all these bounds for deterministic algorithms. Sch oning s algorithm. In 1999 U. Sch oning [17] presented a simple randomized algorithm for k SAT running in time poly(n) 2(k 1) k) n . This algorithm is based on random walks (like Papadimitriou s algorithm [13] for 2 SAT) Namely, given an input formula F in k CNF with n variables, Sch oning s algorithm repeats the following random walk procedure an exponential number of times: 1. Choose an initial assignment A uniformly at random. 2. Repeat 3n times: If the current assignment A satis es F , then ....

C. H. Papadimitriou. On selecting a satisfying truth assignment. In Proceedings of the 32nd Annual IEEE Symposium on Foundations of Computer Science, FOCS'91, pages 163-169, 1991.

....This is true not only for the task of deduction, but also for many other forms of reasoning which have been developed. All those were shown to be even harder to compute than the original formulation [27, 24] Of particular interest in this context are the results on default reasoning tasks [28, 8, 19], where the increase in complexity is clearly at odds with the intuition that reasoning with defaults should somehow reduce the complexity of reasoning. This remains true, even when we severely restrict the expressivity of the knowledge base, the default rules and the queries allowed. An ....

C. H. Papadimitriou. On selecting a satisfying truth assignment. In Proc. 32nd Ann. IEEE Symp. on Foundations of Computer Science, pages 163--169, 1991.

....inadequate for commonsense reasoning. This is true not only for the task of deduction,but also for many other forms of reasoning which have been developed [Selman, 1990; Roth, 1993] Of particular interest in this context are the hardness results on default reasoning tasks [Selman, 1990; Papadimitriou, 1991] where the increase in complexity (relative to corresponding deduction tasks) is clearly at odds with the intuition that reasoning with defaults should somehow re duce the complexity of reasoning. Moreover, many studies in this framework have shown that capturing what people view as ....

....in the examples discussed above. 3.1 Relations to Other Formalisms There is no direct mapping between our treatment of incomplete information and traditional formalisms for default reasoning. As an example, consider the case of preferred interpretations [McCarthy , 1980; Selman and Kautz, 1990; Papadimitriou, 1991] There, a theory F and a set D of defaults are given. The theory defines a set of possible models, and the default rules define a preference relation (a partial order) on those. Once a preferred model is found, inference is done by evaluating queries in this model. While this formalism leads to ....

C. H. Papadimitriou. On selecting a satisfying truth assignment. In Proc. 32nd Ann. IEEE Symp. on Foundations of Computer Science, pages 163--169, 1991.

....there is no complete theoretical explanation for this observation, there is an intuition that it comes from the time required to propagate dependencies through Horn clauses involved in the definitions. It is known that stochastic search solves sets of Horn clauses in expected O(n 2 ) time (Papadimitriou 1991; 1993) The contribution of this paper is to describe a method for improving local search for problems with defined variables. We will describe the architecture of the Dagsat system, in which search concentrates only on the independent variables, and a fast mechanism handles dependent ....

Papadimitriou, C.H. (1991). On selecting a satisfying truth assignment. Proc. of 32th Conference on the Foundations of Computer Science, 1991, 163-- 169.

.... : 1987: Randomized Local search (SAT1) 31, 36] 1987: Parallel local search (SAT1.6) 31, 36] 1988: Local search for n queen [30, 79, 77] 1990: Unison algorithm and hardware [80, 81] 1991: Local search complexity [38, 65] 1991: Local search for 2 SAT [64] 1992: Local search with traps (SAT1.5) 35, 36] 1992: Greedy local search GSAT [73] C o n t i n u o u s 8 : Constrained 8 : 1986: Branch and bound (APEX) 6] 1988: ....

....algorithm is slow under conditions that make the corresponding simplified algorithm slow. A number of special SAT problems, such as 2 satisfiability and Horn clauses, are solvable in polynomial time [1, 15, 63] There are several linear time algorithms [3, 21] and polynomial time algorithms [64, 72] existing. ffl Discrete, unconstrained algorithms. In this approach, the number of unsatisfiable CNF (or satisfiable DNF) clauses is formulated as the value of the objective function, transforming the SAT formula into a discrete, unconstrained minimization problem to the objective function. ....

C.H. Papadimitriou. On selecting a satisfying truth assignment. In Proceedings of the 32nd Annual Symposium of the Foundations of Computer Science, pages 163--169, 1991.

....other forms of reasoning which have been developed, partly in order to avoid the computational difficulties in exact deduction and partly to meet some (psychological and other) plausibility requirements. All those were shown to be even harder to compute than the original formulation (Selman, 1990; Papadimitriou, 1991; Roth, 1996) As a consequence, a lot of recent work in reasoning aims at identifying classes of limited expressiveness, with which one can perform some sort of reasoning efficiently (Levesque and Brachman, 1985; Cadoli, 1995; Levesque, 1992; Selman, 1990) However, none of these works meets the ....

Papadimitriou, C. H. 1991. On selecting a satisfying truth assignment. In Proc. 32nd Ann. IEEE Symp. on Foundations of Computer Science, pages 163--169.

....is defined in the following way: Its nodes are truth assignments to the letters of Gamma, and there is an edge from node M to node M 0 if there is a default fi D 2 Delta such that (a) both M and M 0 satisfy fi; b) M 0 satisfies and M does not; c) M and M 0 differ only in . Papadimitriou [1991] gives a similar definition, the only difference being that the nodes of the graph G( Gamma; Delta) are necessarily models of Gamma. The difference is immaterial if Gamma is a tautology. If there is a path in G( Gamma; Delta) from M to M 0 , then we write M M 0 . Truth assignment M 0 ....

.... Gamma; Delta , find an undominated model. The corresponding problem in the planning framework has not been addressed from the computational point of view. We briefly survey the main results about UNDOMINATEDFIND, focusing on the case Gamma = true: ffl it is in FPSPACE and PSPACE hard [Papadimitriou, 1991]; ffl it is polynomial if for each default fi D 2 Delta the set fi is a singleton [Papadimitriou, 1991] ffl it is polynomial if for each default fi D 2 Delta all literals in fi are positive [Selman and Kautz, 1990] As we saw in Section 2.4, PLANSAT for default STRIPS (i.e. each ....

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C. H. Papadimitriou. On selecting a satisfying truth assignment (extended abstract). In Proceedings of the 32nd Annual Symposium on the Foundations of Computer Science (FOCS-91), pages 163--169, 1991.

.... plus heuristic (DPLH) 65] and a simplified Davis Putnam algorithm with strict ordering of variables [61] A number of special SAT problems, such as 2 satisfiability and Horn clauses, are solvable in polynomial time [1, 14, 79] Several linear time algorithms [3, 25] polynomial time algorithm [80], and polynomial time bound [90] were proposed. ffl Discrete, unconstrained algorithms. In this approach, the number of unsatisfiable CNF clauses or the number of satisfiable DNF clauses is formulated as the value of the objective functions, so the SAT problem is transformed into a discrete, ....

.... 1987: DNF Local search (SAT1.4) 34] 1987: Parallel local search (SAT1.6) 34] 1987: Local search hardware [34] 1988: Local search for n queen problem [33, 97, 98] 1989: Local search backtracking [35, 44, 41] 1990: Unison algorithm [101] 1990: Unison hardware [102] 1991: Local search complexity [48, 80] 1992: GSAT [93] Continuous 8 : Constrained 8 : 1986: Branch and bound (APEX) 5] 1988: Programming models [5, 66] 1988: Cutting Plane [58, 56] 1989: Branch and cut [59] 1990: Interior point method [68] ....

[Article contains additional citation context not shown here]

C.H. Papadimitriou. On selecting a satisfying truth assignment. In Proceedings of the 32nd Annual Symposium of the Foundations of Computer Science, pages 163--169, 1991.

....genotypes contain truth assignments that are randomly initialized. Point crossover is applied in this problem, with panmictic mating. A local search strategy is applied at each step; a random literal is selected from one of the unsatisfied clauses and negated. This is an optimal strategy for SAT [17], and we also use it as a mutation operator. For LS, the energy cost charged for each evaluation is a constant. The energy benefit, however, depends on the fraction of clauses that are satisfied by the agent s truth assignment, and for which there are available resources. Environmental resources ....

C. Papadimitriou. On selecting a satisfying truth assignment. In 32nd FOCS, 1991.

....algorithm, and some complete optimization algorithms [6, 17, 19, 18, 20, 23, 30, 33] The incomplete algorithms can only find one random solution for certain CNF formulas and give no answer if the CNF formula is not satisfiable. Algorithms in this class include the local search algorithms [17, 18, 22, 61] and some programming algorithms [45, 71] Depending on the SAT algorithms used, for the same problem instances, the hard and easy distributions of SAT problem instances are completely different. We use problem instances generated from the exact 3 SAT model as an example. Figure 1 shows, for 50 ....

C.H. Papadimitriou. On selecting a satisfying truth assignment. In Proceedings of the 32nd Annual Symposium of the Foundations of Computer Science, pages 163--169, 1991.

....CNF formulas. Start with a random truth assignment; randomly select a clause not satisfied by this assignment; flip the truth assignment of one of the letters occuring in this clause (the clause becomes satisfied) repeat the last two steps until the assignment satisfies all clauses. Papadimitriou [20] shows that such a surprisingly simple randomized strategy finds assignments for 2CNF formulas in O(n 2 ) steps with probability approaching one, where n is the number of propositional letters. However, this method does not work for general CNF. We therefore propose the following approach, that ....

Papadimitriou, C.H. On selecting a satisfying truth assignment. Proc. of the Conference on the Foundations of Computer Science, 1991, 163--169.

....also for many other forms of reasoning which have been developed, partly in order to avoid the computational difficulties in exact deduction and partly to meet some (psychological and other) plausibility requirements. All those were shown to be even harder to compute than the original formulation [Sel90, Pap91, Rot93]. The same is true for a lot of recent work in reasoning that aims at identifying classes of limited expressiveness, with which one can perform some sort of reasoning efficiently [BL84, Lev92, Sel90] None of these works meet the strong tractability requirements required for common sense reasoning ....

C. H. Papadimitriou. On selecting a satisfying truth assignment. In Proc. 32nd Ann. IEEE Symp. on Foundations of Computer Science, pages 163--169, 1991.

....logic, etc. have inference problems that are even harder: complete for the second level of the polynomial hierarchy, see [ Cadoli and Lenzerini, 1994; Eiter and Gottlob, 1993; Gottlob, 1992 ] model preference default theories [ Selman and Kautz, 1990 ] have even higher complexity [ Papadimitriou, 1991 ] 1c) Finally, weaker versions of the above formalisms provide polynomial time inference at the expense of our next criterion, expressibility. These include Horn clauses [ Dowling and Gallier, 1984 ] Horn model preference defaults [ Selman and Kautz, 1990 ] restricted forms of default ....

C.H. Papadimitriou. On selecting a satisfying truth assignment. Proceedings of FOCS, 1991.

....Davis Putnam. The quasigroup, factorization, and zebra problems have orders of magnitude fewer models despite containing more variables. We speculate that the number of models in relation to problem size may be crucial to the performance of hill climbing procedures. 8 Related Work Papadimitriou [12] proposed a simple random walk algorithm for 2 SAT which repeatedly flips unsatisfied variables chosen at random. For satisfiable problems, this algorithm finds a model in O(N 2 ) flips with probability approaching 1 as N increases. Selman and Kautz proposed adding random walk to Gsat in [14] ....

C.H. Papadimitriou. On selecting a satisfying truth assignment. Proc. Conference on the Foundations of Computer Science, pages 163--169, 1991.

....of CNF formulas. Start with a random truth assignment; randomly select an clause not satisfied by this assignment; flip the truth assignment of one of the letters occuring in this clause (the clause becomes satisfied) repeat the last two steps until the assignment satisfies all clauses. Papadimitriou (1991) shows that such a surprisingly simple randomized strategy finds assignments of 2CNF formulas (satisfiable ones, of course) in O(n 2 ) steps with probability approaching one, where n is the number of propositional letters. His proof exploits properties of random walks (Feynman et al. 1989) ....

....methods for solving hard combinatorial search problems, such as, simulated annealing and genetic algorithms (Davis 1987) In our future research we hope to develop a precise formal understanding of the benefits and applicability of each technique. While some theoretical results, such as those of Papadimitriou (1991) on random walks, suggest that the strategies are plausible, it is likely to be extremely difficult to prove formally that they are effective in practice. 11 Finally, we should note that we do not claim that GSAT will be able to outperform backtracking search methods on all possible problems. We ....

Papadimitriou, C.H. (1991). On Selecting a Satisfying Truth Assignment. Proc. of the Conference on the Foundations of Computer Science, 1991, 163--169.

....of CNF formulas. Start with a random truth assignment; randomly select a clause not satisfied by this assignment; flip the truth assignment of one of the letters occuring in this clause (the clause becomes satisfied) repeat the last two steps until the assignment satisfies all clauses. Papadimitriou (1991) shows that such a surprisingly simple randomized strategy finds assignments for 2CNF formulas in O(n 2 ) steps with probability approaching one, where n is the number of propositional letters. However, this method does not work for general CNF. We therefore propose the following approach, that ....

Papadimitriou, C.H. (1991). On Selecting a Satisfying Truth Assignment. Proc.

....[7] Levesque argues [23, 24] that reasoning with a more direct representation is easier and better suits common sense reasoning. He suggests to represent the knowledge base KB in a vivid form, which bears a strong and direct relationship to the real world. This might be just a model of KB [8, 28] on which one can evaluate the truth value of the query ff. It is not clear, however, how one might derive a vivid form of the knowledge base. Moreover, selecting a model which is the most likely model of the real world, under various reasonable criteria, is computationally hard [28, 32] Most ....

....of KB [8, 28] on which one can evaluate the truth value of the query ff. It is not clear, however, how one might derive a vivid form of the knowledge base. Moreover, selecting a model which is the most likely model of the real world, under various reasonable criteria, is computationally hard [28, 32]. Most importantly, in order to achieve an efficient solution to the reasoning problem this approach modifies the problem: reasoning with a vivid representation no longer solves the problem KB j= ff, but rather a different problem, whose exact relation to the original inference problem depends on ....

C. H. Papadimitriou. On selecting a satisfying truth assignment. In Proc. 32nd Ann. IEEE Symp. on Foundations of Computer Science, pages 163--169, 1991.

....k SAT based on local search Evgeny Dantsin Andreas Goerdt y Edward A. Hirsch z Ravi Kannan x Jon Kleinberg Christos Papadimitriou k Prabhakar Raghavan Uwe Sch oning yy Abstract Local search is widely used for solving the propositional satis ability problem. Papadimitriou [16] showed that randomized local search solves 2 SAT in polynomial time. Recently, Sch oning [20] proved that a close algorithm for k SAT takes time (2 2 k ) n up to a polynomial factor. This is the best known worst case upper bound for randomized 3 SAT algorithms (cf. also [21] We describe a ....

....search is a well known heuristic search method [2, 14, 22] A huge amount of experiments has demonstrated that local search is often very good in solving SAT for many classes of formulas, see [6] for survey. Also, there is a few average case and worstcase bounds for local search in SAT, e.g. [16, 10, 5, 20, 8]. C. H. Papadimitriou showed [16] that 2 SAT can be solved in polynomial time by a randomized local search procedure. Our algorithm is inspired by Sch oning s algorithm [20] which is close to Papadimitriou s algorithm and runs in time poly(n) 2 2 k ) n for k SAT. This is the best known ....

[Article contains additional citation context not shown here]

C. H. Papadimitriou. On selecting a satisfying truth assignment. In Proceedings of the 32nd Annual IEEE Symposium on Foundations of Computer Science, FOCS'91, pages 163-169, 1991.

....k SAT Based on Local Search Evgeny Dantsin Andreas Goerdt y Edward A. Hirsch z Ravi Kannan x Jon Kleinberg Christos Papadimitriou k Prabhakar Raghavan Uwe Sch oning yy Abstract Local search is widely used for solving the propositional satis ability problem. Papadimitriou [16] showed that randomized local search solves 2 SAT in polynomial time. Recently, Sch oning [20] proved that a close algorithm for k SAT takes time (2 2 k ) n up to a polynomial factor. This is the best known worst case upper bound for randomized 3 SAT algorithms. We describe a deterministic ....

....search is a well known heuristic search method [2, 14, 21] A huge amount of experiments has demonstrated that local search is often very good in solving SAT for many classes of formulas, see [6] for survey. Also, there is a few average case and worstcase bounds for local search in SAT, e.g. [16, 10, 5, 20, 8]. C. H. Papadimitriou showed [16] that 2 SAT can be solved in polynomial time by a randomized local search procedure. Our algorithm is inspired by Sch oning s algorithm [20] which is close to Papadimitriou s algorithm and runs in time poly(n) 2 2 k ) n for k SAT. This is the best known ....

[Article contains additional citation context not shown here]

C. H. Papadimitriou. On selecting a satisfying truth assignment. In Proceedings of the 32nd Annual IEEE Symposium on Foundations of Computer Science, FOCS'91, pages 163-169, 1991.

No context found.

C.H. Papadimitriou. On selecting a satisfying truth assignment. FOCS, pages 163--169, 1991.

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C. H. Papadimitriou. On selecting a satisfying truth assignment. In Proc. 32nd IEEE Symp. on the Foundations of Comp. Sci., pages 163-169, 1991.

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C. Papadimitriou. On Selecting a Satisfying Truth Assignment. In Proc. 32nd IEEE Symposium on the Foundations of Computer Science, pages 163{ 169, 1991.

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Papadimitriou CH, On selecting a satisfying truth assignment , Proc. of the Conference on the Foundations of Computer Science 163--169 (1991)

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Papadimitriou, C. H. On selecting a satisfying truth assignment. Proc. FOCS-91, 163-169 (1991).

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Papadimitriou, C. H. On selecting a satisfying truth assignment. In Proceedings of the 32nd Annual IEEE FOCS'91, pages 163-169,

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C. H. Papadimitriou. On selecting a satisfying truth assignment. In 32nd annual ACM Symposium on Foundations of Computer Science, pages 183-- 169, 1991.

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C. H. Papadimitriou, On selecting a satisfying truth assignment, Proc. 32nd IEEE FOCS (1991) 163-169.

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C.H. Papadimitriou. On selecting a satisfying truth assignment (extended abstract). In Proceedings of the 32rd Annual IEEE Symposium on Foundations of Computer Science, San Juan, Puerto Rico, pages 163-169, 1991.

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C.H. Papadimitriou. On Selecting a Satisfying Truth Assignment. In Proceedings of the Conference on the Foundations of Computer Science, pages 163-169, 1991.

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