Cadoli, M., Giovanardi, A., Schaerf, M.: An Algorithm to Evaluate Quantified Boolean Formulae. In: Proc. of the 15th Nat. Conf. on Artificial Intelligence. (1998) 262--267  Home/Search   Document Details and Download   Summary   Related Articles   Check

....are harder than , and thus not polynomially reducible to SAT testing. Moreover, these problems cannot be reduced to any solver for problems that are located in the Polynomial Hierarchy. On the other hand, they are solvable in polynomial space, and thus reducible to a QBF solver (e.g. [4, 32, 8]) in polynomial time. Furthermore, testing probabilistic causal irrelevance is easier than C complete problems, which could perhaps help in finding polynomial time (randomized) approximation algorithms for this problem. We remark that for computing the conditional probability over two causal ....

M. Cadoli, A. Giovanardi, and M. Schaerf. An algorithm to evaluate quantified boolean formulae. In Proceedings AAAI-98, pages 262--267, 1998.

....be utilized for this purpose, or the diagnostic frontend of the DLV system [10] Another possibility would be an encoding of causal explanations in Answer Set Programming, and using the DLV engine to compute solutions. For the case of general causal explanations, reductions to QBF solvers such as [5, 41, 19] could be used. 7.2 Bayesian Networks After Cooper s well known intractability result [7] for probabilistic inference in Bayesian networks, a number of papers in this area have investigated complexity issues for reasoning and in particular for explanation finding. A dominating notion of ....

M. Cadoli, M. Schaerf, A. Giovanardi, and M. Giovanardi. An algorithm to evaluate quantified boolean formulae and its experimental evaluation. Journal of Automated Reasoning, 28:101--142, 2002.

.... are maximum among all such assignments. Q ALL SAT is a special form of a quantified Boolean formula which contains two subformulas in conjunctive normal form (CNF) First solution algorithms for quantified Boolean formulas have been constructed, for example, by Cadoli, Giovanardi, and Schaerf [2] and Rintanen [7] These algorithms consider the case where all quantifiers constitute a prefix of a CNF formula. They cannot be applied to logic based abduction. We will propose algorithms for Q ALL SAT and its related problems that can take advantage of any efficient SAT solver and of any solver ....

Cadoli, M., Giovanardi, A., Schaerf, M.: An Algorithm to Evaluate Quantified Boolean Formulae. Proceedings of the Fifteenth National Conference on Artificial Intelligence (1998)

....and QBF have PSPACE complete decision problems [16, 31] This implies that the two problems are polynomially reducible to each other. A natural reduction from QBF to K is described in [12] In the last few years extensive effort was carried out into the development of highly optimized QBF solvers [17, 5]. One motivation for this effort is the hope of using QBF solvers as generic search engines [25] much in the same way that SAT solvers are being used as generic search engines. This suggests that another approach to K satisfiability is to find a natural reduction of K to QBF, and then apply a ....

....much in the same way that SAT solvers are being used as generic search engines. This suggests that another approach to K satisfiability is to find a natural reduction of K to QBF, and then apply a highly optimized QBF solver. We describe now such a reduction. A similar approach is suggested in [5] without providing either details or results. QBF is an extension of propositional logic with quantifiers. The set of QBF formulas is constructed from a set = fx 1 ; xn g of Boolean variables, and closed under the Boolean connectives and : as well as the quantifier 8x i . As usual, we ....

M. Cadoli, M. Schaerf, A. Giovanardi, and M. Giovanardi. An algorithm to evaluate quantified Boolean formulae and its experimental evaluation. Technical report, Dipartmento di Imformatica e Sistemistica, Universita de Roma, 1999.

....[34; 39] The general mechanism of our approach is to translate (in polynomial time) a given reasoning task into the evaluation problem for QBFs and then use a QBF evaluator to compute the resultant instances. The existence of efficient QBF solvers, such as the systems developed by Cadoli et al. [4] , Giunchiglia et al. 18] Rintanen [32] or Feldmann et al. 15] makes such a rapid prototyping approach practicably applicable. A similar approach for solving various reasoning tasks belonging to the area of nonmonotonic reasoning has been realized in the system QUIP [12; 11; 27] This ....

M. Cadoli, A. Giovanardi, and M. Schaerf. An Algorithm to Evaluate Quantified Boolean Formulae. In Proceedings of the AAAI National Conference on Artificial Intelligence, pages 262--267, Madison, Wisconsin, 1998.

....theorem provers for logics with complexity up to 2 are needed as host for efficient translations. For example, DLV [78] DeRes [23] or a disjunctive extension of smodels [75] which all provide this expressiveness, might be used, as well as theorem provers based on quantified Boolean formulas [20, 83, 32]. However, efficient transformations of the problems to these logics remain to be designed. In the case of problems with complexity P , such translations might not be very appealing, since the theorem provers mentioned above are tailored for solving problems whose complexity characteristics ....

M. Cadoli, A. Giovanardi, and M. Schaerf. An algorithm to evaluate quantified Boolean formulae. In Proc. 16th National Conference on AI (AAAI-98), Madison, WI, pp. 262--267, AAAI Press/MIT Press, 1998.

....based on a reduction approach. The central idea is to translate a given reasoning task into a quantified Boolean formula (QBF) and then applying some sophisticated QBF solver to evaluate the translated QBF. The existence of efficient QBF solvers, like, e.g. the systems developed by Cadoli et al. [5], Giunchiglia et al. 18] Rintanen [37] Letz [25] or Feldmann et al. 15] makes this reduction approach practicably applicable. Concerning the particular reductions, we provide efficient (polynomial time) translations of reasoning tasks for the following modal nonmonotonic logics: Moore s ....

....by the availability of several practicably efficient QBF solvers. Among the different tools, there is a propositional theorem prover, boole, based on binary decision diagrams, a system using a generalised resolution principle [23] several provers implementing an extended Davis Putnam procedure [5, 15, 18, 25, 37], as well as a distributed algorithm running on a PC cluster [15] With the exception of boole, these tools do not accept arbitrary QBFs, but require the input formula to be in prenex conjunctive normal form. To avoid an exponential increase of formula size, structure preserving normal form ....

[Article contains additional citation context not shown here]

M. Cadoli, A. Giovanardi, and M. Schaerf. An Algorithm to Evaluate Quantified Boolean Formulae. In Proc. AAAI-98, pages 262--267, 1998.

....problems e# ciently as well. The other algorithms require only polynomial space, solving 3 CNF QBF and 3 CNF # 2 SAT. Our interest in these special cases stems from the wide interest in 3 SAT algorithms, and the role of 3 CNF # 2 SAT as a canonical problem studied in experimental QBF algorithms [16, 3, 8]. It has been proposed that an easy hard easy phase transition for 3 CNF # 2 SAT occurs at a smaller clause to variable ratio than that for 3 SAT: either when m n 1.4, or m n 2, depending on the procedure used to select random 3 CNF formulas [8] These small threshold values add ....

....depending on the procedure used to select random 3 CNF formulas [8] These small threshold values add significance to our bounds stated in terms of m. 2 Obstacles All non trivial algorithms we could find for PSPACE complete subsets of QBF have only been verified experimentally in the literature [16, 3, 9]. Our research program was to study improved algorithms for SAT, and extract components of these algorithms that work for universally quantified variables. Several obstacles arose. Lack of locality. The technique of local search for a satisfying assignment, given a candidate assignment, has ....

[Article contains additional citation context not shown here]

M. Cadoli, A. Giovanardi, and M. Schaerf, An algorithm to evaluate quantified Boolean formulae, Proceedings of AAAI-98, pp. 262-267, 1998.

.... remained objects of purely theoretical interest for years, and it is only very recently that solvers have been implemented to solve Quantified Boolean Formulae (QBF) All of the algorithms we are aware of either rely on or generalize SAT algorithms, such as resolution [5] Davis Putnam and DLL [7, 18], or backtracking and improvements [14] due to space restrictions we do not cite all recent related publications) In this paper, we propose to study the general problem of quantified constraints over arbitrary finite domains, of which the boolean case is a particular instance. We attempt to ....

M. Cadoli, A Giovanardi, and M. Schaerf. An algorithm to evaluate quantified boolean formulae. In Proc. of the 15th Nat. Conf. on AI (AAAI), pages 262--267, Madison, USA, 1999. AAAI/MIT Press.

....miniscoping and quantifier expansion are also used in Williams et al. 20] to optimize di#erent computation tasks like the calculation of fixed points. Most QBL algorithms generalize the Davis Putnam procedure to operate on formulae transformed into quantified clausal normal form. Cadoli et al. [6] and Rintanen [16, 15] present di#erent heuristic extensions of the Davis Putnam method. Cadoli et al. s techniques were tuned for randomly generated problems and Rintanen s strategies were specially designed for planning problems whose quantifiers have a fixed ### structure. Other work includes ....

Marco Cadoli, Andrea Giovanardi, and Marco Schaerf. An algorithm to evaluate quantified Boolean formulae. In Proceedings of the 15th National Conference on Artificial Intelligence (AAAI-98) and of the 10th Conference on Innovative Applications of Artificial Intelligence (IAAI-98), July 26--30 1998.

.... formulas with a QBF solver has become an attractive and increasingly important research topic over the last years (cf. e.g. 12, 5, 4, 11] The QBFs resulting from the encodings are usually not in a specific normal form which prevents the application of most of the available QBF provers [9, 3, 6, 8, 10, 12] without a translation into normal form. The only kind of QBF solvers which can handle arbitrary formulas is based on binary decision diagrams (BDDs) In order to make more practicably successful QBF solvers available for solving the encoded problems, a transformation of an arbitrary QBF into a ....

M. Cadoli, A. Giovanardi, and M. Schaerf. An Algorithm to Evaluate Quantified Boolean Formulae. In Proceedings of the 15th National Conference on Artificial Intelligence (AAAI-98), pages 262--267, 1998.

....is a much more powerful reasoning method than circumscription, and that it can not be reduced in polynomial time to circumscription. Thus, circumscriptive theorem provers can not be efficiently used for curb reasoning. On the other hand, a curb theorem prover could be based on a QBF solver (see [10, 4, 16, 1, 9]) After proving our main result, we identify classes of theories for which the complexity of curbing is located at a lower complexity level. Specifically, we show that if a 2 theory T has the lub property, that is, every set of good models of T has a least (unique minimal) upper bound, then ....

M. Cadoli, A. Giovanardi, and M. Schaerf. An Algorithm to Evaluate Quantified Boolean Formulae. In Proc. AAAI/IAAI-98, pp. 262--267, 1998.

....SAT solver to solve it) can now compete and even outperform specialized domain dependent solvers. Another area of research is to use the results obtained for SAT algorithms on related domains: computation of implicant cover[SC96] prime implicants implicates [CC96] Quantified Boolean Formulas[CGS98, Rin99] DISTANCE SAT[BM99] etc. Our work follows this idea: we show how to modify the famous Davis and Putnam method to compute some specific part of the implicants. Although the usage of DPLL to compute implicants is not new, we compute implicants minimal with respect of some of their literals ....

Marco Cadoli, Andrea Giovanardi, and Marco Schaerf. An algorithm to evaluate quantified boolean formulae. In Proceedings of the Fifteenth National Conference on Artificial Intelligence (AAAI'98), pages 262-- 267, Madison (Wisconsin - USA), 1998. 10

.... Our complexity results give a clear picture of the feasibility of polynomial time translations for particular planning problems into computational logic systems such as Blackbox [37] CCALC [47] smodels [33] DLV, satisfiability checkers, e.g. 2, 74] or Quantified Boolean Formula (QBF) solvers [4, 61, 18]. INFSYS RR 1843 01 11 1.3 Structure of the Paper The rest of the paper is structured as follows. The next section formally introduces the language K, and provides the syntax and formal semantics of the core language, as well as enhancements of the language by macro constructs that are useful ....

.... for implementation The complexity results have important consequences for the implementation of K on top of existing computational logic systems, such as Blackbox [37] CCALC [47] smodels [33] DLV, satisfiability checkers, e.g. 53, 41, 2, 74] or Quantified Boolean Formula (QBF) solvers [4, 61, 18]. Optimistic Planning under arbitrary plan length is not polynomially reducible to systems with capability of solving problems within the Polynomial Hierarchy, e.g. Blackbox, satisfiability checkers, CCALC, smodels, or DLV, while it is feasible using QBF solvers. On the other hand, for fixed (and ....

M. Cadoli, A. Giovanardi, and M. Schaerf. An Algorithm to Evaluate Quantified Boolean Formulae. In Proceedings AAAI/IAAI-98, pages 262--267, 1998.

....subsumes the other: it is easy to come up with examples in which trivial truth behaves much better than backjumping, and the other way around. In this paper we experimentally evaluate these two optimizations both on randomly generated and on real world test cases. 1 Introduction Trivial truth [1, 2] and backjumping [3] are two optimization techniques that have been proposed for deciding quantified boolean formulas (QBFs) satisfiability. Both these techniques can greatly improve the overall performance of a QBF solver, but they are the expression of two opposite philosophies. On one hand, ....

....is done using the QUBE system [4] While trivial truth is implemented by various QBF solvers like EVALUATE [1] and QSOLVE [5] QUBE is as far as we know the only system with a backjumping optimization built in. The experimental analysis is performed on a combination of random kQBFs (see [2]) generated according to model A proposed by Gent and Walsh in [6] and on the real world instances proposed by Rintanen in [7] The overall conclusions are that on random kQBFs, backjumping becomes more effective as the value of k increases, while trivial truth is more effective for ....

[Article contains additional citation context not shown here]

M. Cadoli, M. Schaerf, A. Giovanardi, and M. Giovanardi. An Algorithm to Evaluate Quantified Boolean Formulae and its Experimental Evaluation. In Highlights of Satisfiability Research in the Year

....subsumes the other: it is easy to come up with examples in which trivial truth behaves much better than backjumping, and the other way around. In this paper we experimentally evaluate these two optimizations both on randomly generated and on real world test cases. 1 Introduction Trivial truth [1, 2] and backjumping [3] are two optimization techniques that have been proposed for deciding quantified boolean formulas (QBFs) satisfiability. Both these techniques can greatly improve the overall performance of a QBF solver, but they are the expression of two opposite philosophies. On one hand, ....

....up with examples in which trivial truth behaves much better than backjumping, and the other way around. In this paper we experimentally compare trivial truth and backjumping. The comparison is done using the QUBE system [4] While trivial truth is implemented by various QBF solvers like EVALUATE [1] and QSOLVE [5] QUBE is as far as we know the only system with a backjumping optimization built in. The experimental analysis is performed on a combination of random kQBFs (see [2] generated according to model A proposed by Gent and Walsh in [6] and on the real world instances proposed ....

[Article contains additional citation context not shown here]

M. Cadoli, A. Giovanardi, and M. Schaerf. An algorithm to evaluate quantified boolean formulae. In Proc. of AAAI, 1998.

....= TRUE (line 21) If such a literal l exists, jlj:mode is set to R SPLIT, and l is returned (line 22) If no such literal exists, NULL is returned (line 23) QUBE returns TRUE if the input QBF is satisfiable, and FALSE otherwise. It is easy to see that QUBE, like other QBF procedures (see, e.g. [4 6]) is a generalization of the Davis, Logemann, Loveland procedure (DLL) for SAT: QUBE and DLL have the same behavior on QBFs without universal quantifiers. 4 QUBE options Consider Figure 1. QUBE ver. 1.0 features backjumping, trivial truth, six different branching heuristics, i.e. ....

....[ verbose] timeout n1 ] memout n2 ] file name . By default, after the simplifications following the branch on an universal variable have been performed, QUBE checks whether the formula obtained from by deleting universal literals is satisfiable. If it is, then is satisfiable [4]. This optimization can produce dramatic speed ups, particularly on randomly generated QBFs (see, e.g. 4] The option tt disables this check. Notice that ours is an optimized version of trivial truth as described in [4] where the check is performed at each branching node. QUBE branching ....

[Article contains additional citation context not shown here]

M. Cadoli, M. Schaerf, A. Giovanardi, and M. Giovanardi. An algorithm to evaluate quantified boolean formulae and its experimental evaluation. Journal of Automated Reasoning, 2000. To appear. Reprinted in [13].

....PSPACE problem, many of these reductions are readily available. For these reasons, we have seen in the last few years the presentation of several implemented decision procedures for QBFs, like QKN [Kleine B uning, H. and Karpinski, M. and Flogel, A. 1995] EVALUATE [Cadoli et al. 1998, Cadoli et al. 2000] DECIDE [Rintanen, 1999b] QUIP [Egly et al. 2000] QSOLVE [Feldmann et al. 2000] Most of the above decision procedures are based on the Davis, Logemann, Loveland procedure (DLL) for propositional satisfiability [Davis et al. 1962] SAT) This is because it is rather easy to extend DLL ....

....while hcondi hblocki, do hblocki while hcondi, ifhcondi hblock1i else hblock2 i have the same interpretation as in the C language. or no simplification is possible (lines 4, 11) The simplifications performed in lines 8 and 10 correspond to Lemmas 6, 4 5 respectively of [Cadoli et al. 1998, Cadoli et al. 2000] ChooseLiteral ( returns a literal l occurring in such that for each atom x occurring to the left of jlj in the prefix of the input QBF, x and :x do not occur in , or x is existential iff l is existential. ChooseLiteral ( also sets jlj:mode to L SPLIT. Backtrack (res) pops ....

[Article contains additional citation context not shown here]

M. Cadoli, M. Schaerf, A. Giovanardi, and M. Giovanardi. An algorithm to evaluate quantified boolean formulae and its experimental evaluation. Journal of Automated Reasoning, 2000. To appear. Reprinted in [Gent et al., 2000] .

....reasoning is the prototypical PSPACE problem, many of these reductions are readily available. For these reasons, we have seen in the last few years the presentation of several implemented decision procedures for QBFs, like QKN [Kleine B uning, H. and Karpinski, M. and Flogel, A. 1995] EVALUATE [Cadoli et al. 1998, Cadoli et al. 2000] DECIDE [Rintanen, 1999b] QUIP [Egly et al. 2000] QSOLVE [Feldmann et al. 2000] Most of the above decision procedures are based on the Davis, Logemann, Loveland procedure (DLL) for propositional satisfiability [Davis et al. 1962] SAT) This is because it is rather ....

....operator. The constructs while hcondi hblocki, do hblocki while hcondi, ifhcondi hblock1i else hblock2 i have the same interpretation as in the C language. or no simplification is possible (lines 4, 11) The simplifications performed in lines 8 and 10 correspond to Lemmas 6, 4 5 respectively of [Cadoli et al. 1998, Cadoli et al. 2000] ChooseLiteral ( returns a literal l occurring in such that for each atom x occurring to the left of jlj in the prefix of the input QBF, x and :x do not occur in , or x is existential iff l is existential. ChooseLiteral ( also sets jlj:mode to L SPLIT. ....

[Article contains additional citation context not shown here]

M. Cadoli, A. Giovanardi, and M. Schaerf. An algorithm to evaluate quantified boolean formulae. In Proc. AAAI, 1998.

....of formulae. The additional conciseness lifts the complexity of evaluating QBF to PSPACE, which is in strong contrast to the NP hardness of propositional satisfiability. However, the connection between the two problems is close, and not surprisingly some of the recent procedures for evaluating QBF [2, 10] are extensions of the Davis Putnam procedure [3] An alternative solution technique is to reduce a QBF to an unquantified propositional formula, and to test its truth by a conventional satisfiability algorithm. The drawback of this reductive approach is that the size of the propositional formula ....

M. Cadoli, A. Giovanardi, and M. Schaerf. An algorithm to evaluate quantified Boolean formulae. In Proceedings of the Fifteenth National Conference on Artificial Intelligence (AAAI-98) and the Tenth Conference on Innovative Applications of Artificial Intelligence (IAAI-98), pages 262--267. AAAI Press, July 1998.

....become an established method to guarantee that a cipher has such desirable properties. Other problems involving SAT testing in QBF regard the automatic search for existence of weak keys or semi weak keys, or keys which can decrypt any data. A preliminary test has been done using the algorithm in [15] but it didn t returned in one hour. New tests with an enhanced version of the algorithm that exploits defined variables are in preparation. Problem 4 Develop heuristic techniques for propositional reasoning and search that work with every Feistel type cipher with data independent permutations ....

Marco Cadoli, Andrea Giovanardi, and Marco Schaerf. An algorithm to evaluate quantified boolean formulae. In Proceedings of the 15th National Conference on Artificial Intelligence (AAAI-98), 1998. To appear.

....is that it is now possible to use custom algorithms and techniques for, e.g. vertex cover, to decide the tests to be performed in looking for an explanation. For more complex problems, like finding the root of an optimal tree program, techniques for solving general PSPACE problems can be used [1]. We are now considering special cases in which providing verification programs could be simpler. However, high complexity in computing a verification program might not be a problem, if we assume that it can be computed off line. Finally, let us relate our work with that of McIlraith [6] who ....

M. Cadoli, A. Giovanardi, and M. Schaerf, `An algorithm to evaluate quantified boolean formulae', in Proc. of AAAI'98, pp. 262--267. AAAI Press/The MIT Press, (1998).

....provers for logics with complexity up to P 2 are needed as host for efficient translations. For example, DLV [78] DeRes [23] or a disjunctive extension of smodels [75] which all provide this expressiveness, might be used, as well as theorem provers based on quantified Boolean formulas [20, 83, 32]. However, efficient transformations of the problems to these logics remain to be designed. In the case of problems with complexity P NP or P NP k , such translations might not be very appealing, since the theorem provers mentioned above are tailored for solving problems whose complexity ....

M. Cadoli, A. Giovanardi, and M. Schaerf. An algorithm to evaluate quantified Boolean formulae. In Proc. 16th National Conference on AI (AAAI-98), Madison, WI, pp. 262--267, AAAI Press/MIT Press, 1998.

....the previous results for DLP and di#er considerably for TA because they were performed on a di#erent version of the systems. 300 An Analysis of Empirical Testing for Modal Decision Procedures branch d4 dum grz lin path ph poly t4p K p n p n p n p n p n p n p n p n p n leanK 2. 0 1 0 1 1 0 0 0 4 2 0 3 1 2 0 0 0 #KE 13 3 13 3 4 4 3 1 2 17 5 4 3 17 0 0 3 LWB 1 0 6 7 8 6 13 19 7 13 11 8 12 10 4 8 8 11 8 7 TA 9 9 18 20 20 6 9 16 17 19 KSAT 8 8 8 5 11 17 3 4 8 5 5 13 12 10 18 SAT 1.2 12 8 12 Crack 1.0 2 1 2 3 3 1 5 2 2 6 2 3 ....

....di#er considerably for TA because they were performed on a di#erent version of the systems. 300 An Analysis of Empirical Testing for Modal Decision Procedures branch d4 dum grz lin path ph poly t4p K p n p n p n p n p n p n p n p n p n leanK 2. 0 1 0 1 1 0 0 0 4 2 0 3 1 2 0 0 0 #KE 13 3 13 3 4 4 3 1 2 17 5 4 3 17 0 0 3 LWB 1 0 6 7 8 6 13 19 7 13 11 8 12 10 4 8 8 11 8 7 TA 9 9 18 20 20 6 9 16 17 19 KSAT 8 8 8 5 11 17 3 4 8 5 5 13 12 10 18 SAT 1.2 12 8 12 Crack 1.0 2 1 2 3 3 1 5 2 2 6 2 3 1 1 Kris 3 3 8 6 15 13 6 9 3 ....

[Article contains additional citation context not shown here]

M. Cadoli, A. Giovanardi, and M. Schaerf. An algorithm to evaluate quantified Boolean formulae. In Proc. of the 15th National Conference on Artificial Intelligence (AAAI-98), pages 262--267. AAAI Press, 1998.

.... as an extension of the Davis Putnam procedure for the satisfiability of formulae in the propositional logic (Davis, Logemann, Loveland, 1962) It is straightforward to extend the Davis Putnam procedure to handle universal quantifiers; one such extension and some improvements are described by Cadoli et al. 1998). First the variables quantified by the outermost quantifier are considered, then the variables by the second quantifier, and so on. Existential variables correspond to or nodes in the search tree, universal variables correspond to and nodes. The basic algorithm is given in Figure 6. The first ....

Cadoli, M., Giovanardi, A., & Schaerf, M. (1998). An algorithm to evaluate quantified Boolean formulae. In Proceedings of the Fifteenth National Conference on Artificial Intelligence (AAAI-98) and the Tenth Conference on Innovative Applications of Artificial Intelligence (IAAI-98), pp. 262--267.

....formulae has been investigated by Kleine Buning et al. 1995 ] who define a resolution rule for quantified Boolean formulae and a polynomial time decision procedure for quantified Horn clauses. Aspvall et al. 1979 ] give a polynomial time decision procedure for quantified 2 literal clauses. Cadoli et al. 1998 ] extend the Davis Putnam procedure to handle quantified Boolean formulae. Their algorithm is similar to the one in Section 3. Cadoli et al. generalize techniques familiar from the DavisPutnam procedure to QBF. For example, they introduce the pure literal rule for universal variables and a rule ....

M. Cadoli, A. Giovanardi, and M. Schaerf. An algorithm to evaluate quantified Boolean formulae. In Proceedings of the Fifteenth National Conference on Artificial Intelligence (AAAI-98) and the Tenth Conference on Innovative Applications of Artificial Intelligence (IAAI-98), pages 262--267, July 1998.

....; K; vC ) the interesting variables are only K. For instance, in the case of the DES encoding we have only 56 control variables. Other interesting properties can be captured if we use validity or quantified boolean formulae (QBF) for which efficient algorithms also exists [ Buning et al. 1995; Cadoli et al. 1998 ] If we use QBF, finding a key corresponds to a constructive proof of 9K: 0 n j=1 E(vC j ; K; v P j ) 1 A The first property we might wish to prove is the absence of weak keys. Recall that a key is weak if for all plaintexts P one has EK(EK (P) P. In other words a key is weak ....

M. Cadoli, A. Giovanardi, and M. Schaerf. An algorithm to evaluate quantified boolean formulae. In Proceedings of the 15th National Conference on Artificial Intelligence (AAAI98) , pages 262--267. AAAI Press/The MIT Press, 1998.

....only needs to deal with existential quantifiers. The algorithm described in this section paper.tex; 2 08 1999; 17:08; p.13 14 Littman, Majercik, and Pitassi can be viewed as an extension of the DPLL algorithm to Extended SSat by providing pruning rules for universal and randomized quantifiers. Cadoli, Giovanardi, Schaerf (1998) provide a set of pruning rules for universal quantifiers (for solving QBF problems) the purification and unit propagation pruning rules described here are introduced and justified there. Birnbaum Lozinskii (1999) describe a similiar adaptation to DPLL for counting satisfying assignments. ....

Cadoli, M.; Giovanardi, A.; and Schaerf, M. 1998. An algorithm to evaluate quantified Boolean formulae. In Proceedings of the Fifteenth National Conference on Artificial Intelligence (AAAI-98), 262--267. The AAAI Press/The MIT Press.

....fully enumerated. DPLL is designed to solve Sat problems, and, thus, only needs to deal with existential quantifiers. The algorithm described in this section can be viewed as an extension of the DPLL algorithm to Extended SSat by providing pruning rules for universal and randomized quantifiers. Cadoli, Giovanardi, Schaerf (1998) provide a set of pruning rules for universal quantifiers (for solving QBF problems) the purification and unit propagation pruning rules described here are introduced and justified there. Birnbaum Lozinskii (1999) describe a similar adaptation to DPLL for counting satisfying assignments. The ....

Cadoli, M.; Giovanardi, A.; and Schaerf, M. 1998. An algorithm to evaluate quantified Boolean formulae. In Proceedings of the Fifteenth National Conference on Artificial Intelligence (AAAI-98), 262--267. The AAAI Press/The MIT Press.

....related KR formalism or logic, or by designing genuine algorithms. Su s CS program [49] and Doherty et al. s DLS algorithm [16, 28] which handle the case of predicate logic, are incomplete in general and presumably not highly efficient in the propositional context. The use of QBF solvers (e.g. [11, 44, 23]) is here a suggestive starting point for obtaining more suitable systems. As we believe, addressing these issues is worthwhile since nesting circumscriptions is a natural generalization of circumscription, and yields, as shown by our results, a simple yet expressive knowledge representation ....

M. Cadoli, M. Schaerf, A. Giovanardi, and M. Giovanardi. An algorithm to evaluate quantified Boolean formulae and its experimental evaluation. Journal of Automated Reasoning, 28:101--142, 2002.

....of instances seems to grow regularly wrt the depth of QBFs; ffl concerning methodological aspects, we highlight some issues that should be taken into account when comparing difficulty of problems belonging to different classes. The experiments were run using the algorithm Evaluate, presented in (Cadoli, Giovanardi, Schaerf 1998; Cadoli et al. 1999) Evaluate is a generalization of the Davis Putnam procedure for SAT, and is guaranteed to work in polynomial space. Implementations of the Davis Putnam procedure are still among the most efficient complete algorithms for SAT. Like the DavisPutnam procedure, Evaluate exploits ....

Cadoli, M.; Giovanardi, A.; and Schaerf, M. 1998. An algorithm to evaluate quantified boolean formulae. In Proc. of AAAI'98, 262--267.

....wrt the depth of QBFs; ffl concerning methodological aspects, we highlight some issues that should be taken into account when comparing difficulty of problems belonging to different classes. The experiments were run using the algorithm Evaluate, presented in (Cadoli, Giovanardi, Schaerf 1998; Cadoli et al. 1999). Evaluate is a generalization of the Davis Putnam procedure for SAT, and is guaranteed to work in polynomial space. Implementations of the Davis Putnam procedure are still among the most efficient complete algorithms for SAT. Like the DavisPutnam procedure, Evaluate exploits the idea of ....

....when all other simplifying rules fail. Of course, the different nature of evaluation of QBF and SAT forced us to use specific rules in the design of Evaluate, for example, variables bound by the external quantifier must be dealt with before others. More details on the algorithm can be found in (Cadoli et al. 1999). Evaluate and the programs for the generation of random instances are available at www.dis.uniroma1.it cadoli projects QBF Preliminaries QBFs and complexity classes A QBF has the form Q 1 x 1 Delta Delta Delta Qnxn E(x 1 ; xn ) 1) where E is a propositional formula involving the ....

Cadoli, M.; Schaerf, M.; Giovanardi, A.; and Giovanardi, M. 1999. An algorithm to evaluate quantified boolean formulae and its experimental evaluation.

....such as phase transition and easy hard easy distribution. 1 Introduction Interest in algorithms for the SAT problem has been constant in the AI community. SAT is obviously relevant to AI, and, being the prototypical NP complete problem, Parts of this work appeared in a preliminary form in [5, 6] 1 challenges our ability to reason effectively in the presence of large knowledge bases. Usage of algorithms for SAT for reasoning tasks different from classical propositional reasoning has been recently emphasized in the literature. For example, real world problems such as many forms of ....

....in [1] Evaluate is a generalization of the Davis Putnam procedure 2 for SAT, and is guaranteed to work in polynomial space. Implementations of the Davis Putnam procedure are still among the most efficient complete algorithms for SAT. Like the Davis Putnam procedure, Evaluate (first shown in [6]) exploits the idea of performing unit propagation as much as possible, and resorts to branching when all other simplifying rules fail. Of course, the different nature of evaluation of QBF and SAT forced us to use specific rules in the design of Evaluate, for example, variables bound by the ....

Marco Cadoli, Andrea Giovanardi, and Marco Schaerf. An algorithm to evaluate quantified boolean formulae. In Proceedings of the Fifteenth National Conference on Artificial Intelligence (AAAI'98), pages 262--267, 1998.

No context found.

Cadoli, M., Giovanardi, A., Schaerf, M.: An Algorithm to Evaluate Quantified Boolean Formulae. In: Proc. of the 15th Nat. Conf. on Artificial Intelligence. (1998) 262--267

No context found.

M. Cadoli, A. Giovanardi, and M. Schaerf. An algorithm to evaluate quantified boolean formulae. In AAAI '98/IAAI '98: Proceedings of the fifteenth national/tenth conference on Artificial 11 intelligence/Innovative applications of artificial intelligence, pages 262--267. American Association for Artificial Intelligence, 1998.

No context found.

M. Cadoli, A. Giovanardi, and M. Schaerf. An algorithm to evaluate quantified Boolean formulae. In Proceedings of the 15th National Conference on Artificial Intelligence (AAAI '98), pages 262--267, Madison, Wisconsin, 1998.

No context found.

Cadoli, M., Giovanardi, A., Schaerf, M.: An algorithm to evaluate quantified Boolean formulae. In: AAAI-98. (1998) 262--267 http://www.dis.uniroma1.it/pub/AI/papers/cado-giov-scha-98.ps.gz.

No context found.

M. Cadoli, M. Schaerf, A. Giovanardi, and M. Giovanardi, `An algorithm to evaluate quantified boolean formulae and its experimental evaluation ', Journal of Automated Reasoning, 28(2), 101--142, (2002).

No context found.

M. Cadoli, M. Schaerf, A. Giovanardi, and M. Giovanardi, `An algorithm to evaluate quantified boolean formulae and its experimental evaluation', Journal of Automated Reasoning, 28(2), 101--142, (2002).

No context found.

M. Cadoli, A. Giovanardi, and M. Schaerf. An Algorithm to Evaluate Quantified Boolean Formulae. In Proc. AAAI-98, pages 262--267, 1998.

No context found.

M. Cadoli, A Giovanardi, and M. Schaerf. An algorithm to evaluate quantified boolean formulae. In Proc. of the 15th Nat. Conf. on Artificial Intelligence (AAAI), pages 262--267, Madison, USA, 1999. AAAI/MIT Press. See also extended version (Tech Report DIS 08-99).

No context found.

Cadoli, M., Giovanardi, A., Schaerf, M.: An algorithm to evaluate quantified Boolean formulae. In: AAAI-98. (1998) 262--267

No context found.

Cadoli, M.; Giovanardi, A.; and Schaerf, M. 1998. An algorithm to evaluate quantified boolean formulae. In Proceedings of AAAI-98, 262--267.

No context found.

Cadoli, M., Giovanardi, A., Schaerf, M.: An algorithm to evaluate quantified Boolean formulae. In: AAAI-98. (1998) 262--267

No context found.

M. Cadoli, A. Giovanardi, and M. Schaerf. An algorithm to evaluate quantified Boolean formulae. In Proceedings of the 15th National Conference on Artificial Intelligence (AAAI-98), pages 262--267. AAAI Press, 1998.

No context found.

Cadoli, M., Schaerf, M., Giovanardi, A., Giovanardi, M.: An algorithm to evaluate quantified boolean formulae and its experimental evaluation. Journal of Automated Reasoning 28 (2002) 101--142

No context found.

M. Cadoli, A. Giovanardi, and M. Schaerf. An Algorithm to Evaluate Quantified Boolean Formulae. In Proc. AAAI-98, pages 262--267. AAAI Press, 1998.

No context found.

M. Cadoli, A. Giovanardi, and M. Schaerf. An algorithm to evaluate quantified Boolean formulae. In AAAI-98, pages 262--267, 1998.

No context found.

M. Cadoli, A. Giovanardi, and M. Schaerf. An algorithm to evaluate quantified boolean formulae. In Proceedings of the Fifteenth National Conference on Artificial Intelligence (AAAI-98), pages 263--267, 1998.

No context found.

Cadoli, M., A. Giovanardi, and M. Schaerf: 1998, `An Algorithm to Evaluate Quantified Boolean Formulae'. In: Proceedings of the 15th National Conference on Artificial Intelligence (AAAI'98). pp. 262--267.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC