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Determining possible avenues of approach using ANTS - Svenson, Sidenbladh (2003) (1 citation) (Correct)
....locations the enemy objects can reach within certain time limits, given the terrain and the estimated mobility capabilities of the enemy objects. In section 3 we describe how the algorithm works. Many important optimization problems can not be solved exactly in an efficient way (see, e.g. [2, 3]) For many problems there are, however, fast, approximate methods that will in most cases give a solution that is good enough . One such algorithm, building on ideas from biology, is ant colony optimization (ANTS) 4, 5] In nature, ants communicate by deploying pheromone (smell) paths that ....
Christos H. Papadimitriou. Computational Complexity. Addison-Wesley, Reading, MA, 1994.
On the Computational Complexity of Assumption-Based.. - Dimopoulos, Nebel, Toni (2002) (Correct)
....that decides a problem in C. In general, for any class X defined by resource bounds, X denotes the class of problems decidable on a Turing machine with a resource bound given Good textbooks covering the notions we introduce here have been written by Garey and Johnson [13] and Papadimitriou [24]. by X and an oracle for a problem in C. Based on these notions, the sets k , k , and k are defined as follows: 0 = 0 = 0 = P k 1 = NP ; k 1 = co NP ; k 1 = P k The canonical complete problems are SAT for 1 =NP and k QBF for (k 1) where ....
Christos H. Papadimitriou. Computational Complexity. Addison-Wesley, Reading, MA, 1994.
Measuring the Similarity of Labeled Graphs - Champin, Solnon (Correct)
....between two graphs G 1 and G 2 , one has to nd the mapping m that maximizes the score function score(m) f(descr(G 1 ) um descr(G 2 ) g(splits(m) This problem is highly combinatorial. Indeed, it is more general than, e.g. the subgraph isomorphism problem which is known to be NP complete [12]. In this section, we rst study the tractability of a complete search, and then propose a greedy incomplete algorithm for it. 4.1 Tractability of a complete search The search space of the maximum similarity problem is composed of all di erent mappings all subsets of V 1 V 2 and it contains ....
Christos H. Papadimitriou. Computational complexity. Addison-Wesley, Boston, MA (US), 1994.
Testing, Evaluation and Performance of Optimization.. - Whitley, Watson.. (2002) (Correct)
....by a Boolean function. So rather than using logical ANDing to combine disjunctive clauses, the Boolean evaluations associated with the individual clauses are summed with true being 1 and false being 0. The maximum is then sought to solve the problem. This evaluation function is called MAXSAT [11]. Like MAXSAT test problems, Permutation Flowshop Scheduling Problems are often randomly generated. For MAXSAT, these problems are chosen with a particular clause variable ratio that empirically results in difficult problems [9] 14] For permutation flow shop problems, there appears to be even ....
Christos H. Papadimitriou. Computational Complexity. Addison-Wesley Publishing, Co., 1994. Testing Optimization Systems 13
Solving the Sabotage Game is PSPACE-hard - Löding, Rohde (2003) (Correct)
....the x i with i odd is displayed in Fig. 2. We are assuming that the run reaches this gadget at vertex A at the first time. Vertex B is intended to be the exit. In the complete construction Without loss of generality we consider only formulas beginning with an existential quantifier. See for [Pap94], p. 460. 7 there are also edges from X i , resp. X i leading to the last gadget of the graph, represented as dotted lines labelled by back. We will see later that taking these edges as a shortcut, starting from the directly to the last gadget is useless for the Runner. The only meaningful ....
Christos H. Papadimitriou. Computational Complexity. Addison--Wesley, 1994.
Some New Randomized Approximation Algorithms - Andersson (2000) (1 citation) (Correct)
....and it was shown by Arora et al. 14] that the inclusion is strict unless P = NP. De#nition 2.9. Max SNP is the class of NP optimization problems that can be writtenintheform x :#(I,S,x) where # is a quanti#er free formula, I an instance and S a solution. This class is called Max SNP 0 in [72]. This de#nition was inspired by Fagin s characterization of NP [30] It is general enough for Max SNP to contain many natural problems. For instance, the Max Cut problem is in Max SNP since it can be expressed as S#V (x, y) E(x, y) S(x) #S(y) where E(x, y) is true if there is an ....
Christos H. Papadimitriou. Computational complexity. Addison Wesley, Reading, 1994.
The DLV System for Planning with Incomplete Knowledge - Polleres (2001) (Correct)
....coNP. This shows the membership parts. 2 hardness in case (a) is shown by a reduction from deciding whether a quanti ed Boolean formula (QBF) 8X9Y is true, where X;Y are disjoint sets of variables and = C 1 : C k is a CNF over X [ Y . This problem is wellknown 2 complete, cf. [47]. Without loss of generality, we may assume that is satis ed if all atoms in X [ Y are set to true. The initially section contains the following constraints: caused 0 The always section contains the following rules. Suppose that L i;1 , L i;n i are all literals over atoms from X ....
.... (b) Hence, it follows that the problem is in 3 in case (a) and in in case (b) For the hardness part of (a) we transform deciding the validity of a QBF = 9Z8X9Y , where X;Y; Z are disjoint sets of variables and = C 1 : C k is a CNF over X [ Y [ Z, which is 3 complete [47], into this problem. The transformation is in spirit of the reduction in the proof of Theorem 3. The initially section of the K program for PD contains the following caused 0. We introduce, for each atom z i 2 Z, an action set z i , which has the following executability condition: ....
Christos H. Papadimitriou. Computational Complexity. Addison-Wesley, 1994.
A Guided Tour Through Some Extensions Of The Event.. - Cervesato, Franceschet.. (2000) (1 citation) (Correct)
....the worst case computational complexity of model checking in the proposed event calculi. The analysis is based on the model theoretic characterization of the various event calculi provided in Sections 2 and 3. We assume the reader to be familiar with the basics of computational complexity theory [Pap94]. We only remind the definition of polynomial hierarchy. The complexity class P (resp. NP ) contains all the problems for which there exists a deterministic (resp. non deterministic) polynomial time algorithm that makes a number calls to an NP oracle that is polynomial in the size of the ....
....certification has polynomial time complexity. The certificate is the extension w # of w in which # holds. Any yes instance has this certificate. The test w # # is polynomial by Theorem 5.1. In order to prove that the considered problem is NP hard, we define a (polynomial) reduction of 3SAT [Pap94] into the # MPEC problem. 16 Let q be a boolean formula in 3CNF, p 1 , p 2 , and p n be the propositional variables that occur in q, and q = c 1 c 2 . c m , where c i = l i,1 l i,2 l i,3 and, for each l i,j , either l i,j = p k or l i,j = k , for some k. We define a ....
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Christos Papadimitriou. Computational Complexity. Addison-Wesley, 1994.
The Complexity of Model Checking in Modal Event Calculi with.. - Cervesato (1997) (1 citation) (Correct)
....over E and # and formula in (QCMEC) then qcmec, #H#, #o# holds # i# ; o #. 5 Complexity Analysis This section is dedicated to studying the complexity of the various modal event calculi presented in Section 2. We assume the reader familiar with computational complexity theory [12]. Given an EC structure a knowledge WH and a formula # relative to any of the modal event calculi presented in Section 2, we want to characterize the complexity of the problem of establishing whether # is true, which is an instance of the general problem of model checking. We model our ....
....if all points (resp. at least one point) from i to iv of Definition 2.2 hold (resp. does not hold) Finally, if # = e 1 e 2 (resp. # = 1 e 2 ) the algorithm accepts if and only if e 1 w e 2 (resp. e 1 # w e 2 ) It follows, from the definition of acceptance of alternating machines [12], that a CMEC instance (H, #, w) is accepted if and only if I #. model checking in CMEC in AP. Since AP = PSPACE [12] it is in PSPACE. define a (polynomial) reduction of QSAT [12] into CMEC . 14 1 . 2 . 3 . quantified Boolean formula where the quantifiers alternate, so that ....
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Christos Papadimitriou. Computational Complexity. Addison-Wesley, 1994. 18
Entropy Measures and Unconditional Security in Cryptography - Cachin (1997) (13 citations) (Correct)
....its size. But this trade off between the size of the output and its uniformity is not strict, as Y 4 in Example 4.1 shows. The example hints also at the difficulty of finding the best smoothing function for a given distribution. In fact, it is easy to see that Bin Packing, which is NP complete [Pap94] can be reduced to our problem. Bin Packing is the problem of deciding whether n positive integers (or items) can be partitioned into b subsets (or bins) such that the sum of every subset is at most c. So far, only fixed length outputs have been considered. Could a function with ....
Christos H. Papadimitriou, Computational complexity, Addison-Wesley, Reading, 1994.
The Church-Turing Thesis - Sicard, Vélez (1999) (Correct)
....that there are e ectively computable functions which may not be humanly computable has nothing to do with Church s thesis. 18, p. 202] In general, we can say that problem of number of steps, there is not problem for computability, there is a problem for an area called computational complexity [14, 23]. Another possibility for refutation is to eliminate the equivalence in the other direction, it means: If a function f is e ectively calculable do not imply that function f is Turing computable. This function is de ned as: A(0;y) y 1; A(x 1; 0) A(x; 1) A(x 1; y 1) A(x;A(x ....
Christos Papadimitriou, Computational Complexity, Adisson-Wesley, 1994.
Automated Mechanism Design: Complexity Results Stemming.. - Conitzer, Sandholm (2003) (1 citation) (Correct)
....agent, our mechanism can be made to coincide with the Clarke mechanism by subtracting a constant payment max o#O v(o) from that agent. Unfortunately, the problem turns out to remain for general objective functions. To demonstrate we reduce from the INDEPENDENT SET problem, which is [13]. Definition 7 (INDEPENDENT SET) We are given an undirected graph (V, E) with no self loops, that is, edges that begin and end at the same node) and an integer k. We are asked whether there is some I V of size at least k such that no two elements of I have an edge between them. We are now ....
Christos H Papadimitriou. Computational Complexity. Addison-Wesley, 1995.
Non-approximability of Decentralized Control - Rabinovich, Campus, Ram, Goldman (2002) (Correct)
....the same single global utility function (i.e. the result will be a joint policy of action) The study of Dec POMDPs showed that finding an exact optimal joint policy of behavior is NEXP hard. This lower complexity bound, proven in [4] is based on a reduction from a NEXP problem, Wang tiling [16]. Unfortunately, it is problematic to define an approximation to the tiling problem. The difficulty follows from the complicated connections between the number of possible tilings, and the amount and the location of the allowed errors in a tiling relation. Thus, the reduction to tiling is ....
....from MIPs by definition. Moreover, the environment s behavior in multi agent systems may be too complex to be captured by a polynomial time Turing machine Note that probabilistic Turing machines limited to O(1) working tape space are essentially probabilistic finite automata, that is pfa s [16, 7]. as assumed in MIPs. However, in most practical applications the dynamics of the environment can be simulated by a time limited computation as represented by a verifier in MIPs. So MIPs can be seen as a model for a multi agent system, limited in communication and environmental complexity, but ....
Christos H. Papadimitriou. Computational Complexity. Addison-Wesley, 1994.
Polynomial-Length Planning Spans the Polynomial Hierarchy - Turner (2002) (5 citations) (Correct)
....to assume that init(F ) j= state(F ) We will focus on plans whose length is bounded by a polynomial in the input size. 2.3 The Polynomial Hierarchy and PSPACE For our purposes, it is convenient to characterize complexity classes in terms of second order propositional logic. See, for instance, [13]. Consider quanti ed boolean formulas (QBFs) of the form Q 1 x 1 Q 2 x 2 Q k x k (x 1 ; x 2 ; x k ) 2) where (i) each of x 1 ; x 2 ; x k stands for a tuple of propositional variables, ii) each of Q 1 ; Q 2 ; Q k stands for a quanti er, with each Q i 1 di erent ....
.... Roughly speaking, after quanti ers over actions are eliminated from (6) we are left with a disjunction of a polynomially many unambiguous sat problems (which ask: Is a propositional theory with at most one model satis able ) This problem is thought to be beyond P without being NP hard [13]. On the other hand, when plan length is xed the complexity of conformant planning drops for nonconcurrent domains. Theorem 8. For nonconcurrent domains: i) Conformant planning for plans of length 1 is 2 hard. ii) Conformant planning for plans of xed length is 2 complete. ....
Christos Papadimitriou. Computational Complexity. Addison Wesley, 1994.
Algorithms for Sequential Decision Making - Littman (1996) (62 citations) (Correct)
....equal NPT If P=NP, then all the classes in Figure 1.4 from NP complete down to NC have efficient algorithms. If PNP, then the classes from NP complete up to EXPTIME do not have efficient algorithms. Additional background information on complexity classes can be found in Papadimitriou s textbook [115] and the summary in Section A.1. 20 1.3.3 Reinforcement learning Algorithms In a reinforcement learning scenario, the agent must solve the same basic problem faced in planning, but must do so without a correct description of the environment. As a result, the range of choices for evaluating ....
....a such that (O, a, O ) i and R (O, a) O, false, if t 1 and there is no D such that zpath(D, D , rt 21) zpath(D , D , Lt 2J) true, otherwise. It is not hard to see that the above expression for zpath is correct; that it can be evaluated in polynomial space follows from Savitch s Theorem [115]. Since V (D0) is true if and only if the deterministic infinite horizon POMDP has a zero reward policy, and V (D0) can be evaluated in polynomial space, the problem of solving boolean reward POMDPs is in PSPACE. 6.3.3 Stochastic Transitions When a POMDP has stochastic transitions, the set of ....
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Christos H. Papadimitriou. Computational Complexity. Addison-Wesley, Read- ing, Massachusetts, 1994.
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