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The Complexity of Decentralized Control of Markov Decision Processes
 Mathematics of Operations Research
, 2000
"... We consider decentralized control of Markov decision processes and give complexity bounds on the worstcase running time for algorithms that find optimal solutions. Generalizations of both the fullyobservable case and the partiallyobservable case that allow for decentralized control are described. ..."
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Cited by 287 (46 self)
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We consider decentralized control of Markov decision processes and give complexity bounds on the worstcase running time for algorithms that find optimal solutions. Generalizations of both the fullyobservable case and the partiallyobservable case that allow for decentralized control are described. For even two agents, the finitehorizon problems corresponding to both of these models are hard for nondeterministic exponential time. These complexity results illustrate a fundamental difference between centralized and decentralized control of Markov decision processes. In contrast to the problems involving centralized control, the problems we consider provably do not admit polynomialtime algorithms. Furthermore, assuming EXP NEXP, the problems require superexponential time to solve in the worst case.
The Convenience of Tilings
 In Complexity, Logic, and Recursion Theory
, 1997
"... Tiling problems provide for a very simple and transparent mechanism for encoding machine computations. This gives rise to rather simple master reductions showing various versions of the tiling problem complete for various complexity classes. We investigate the potential for using these tiling proble ..."
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Cited by 36 (0 self)
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Tiling problems provide for a very simple and transparent mechanism for encoding machine computations. This gives rise to rather simple master reductions showing various versions of the tiling problem complete for various complexity classes. We investigate the potential for using these tiling problems in subsequent reductions showing hardness of the combinatorial problems that really matter. We ilustrate our approach by means of three examples: a short reduction chain to the Knapsack problem followed by a Hilbert 10 reduction using similar ingredients. Finally we reprove the Deterministic Exponential Time lowerbound for satisfiablility in Propositional Dynamic Logic. The resulting reductions are relatively simple; they do however infringe on the principle of orthogonality of reductions since they abuse extra structure in the instances of the problems reduced from which results from the fact that these instances were generated by a master reduction previously. 1 Introduction This paper...
ViewBased Query Containment
 In Proc. of PODS 2003
, 2003
"... Query containment is the problem of checking whether for all databases the answer to a query is a subset of the answer to a second query. In several data management tasks, such as data integration, mobile computing, etc., the data of interest are only accessible through a given set of views. In this ..."
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Cited by 18 (5 self)
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Query containment is the problem of checking whether for all databases the answer to a query is a subset of the answer to a second query. In several data management tasks, such as data integration, mobile computing, etc., the data of interest are only accessible through a given set of views. In this case, containment of queries should be determined relative to the set of views, as already noted in the literature. Such a form of containment, which we call viewbased query containment, is the subject of this paper. The problem comes in various forms, depending on whether each of the two queries is expressed over the base alphabet or the alphabet of the view names. We present a thorough analysis of viewbased query containment, by discussing all possible combinations from a semantic point of view, and by showing their mutual relationships. In particular, for the two settings of conjunctive queries and twoway regular path queries, we provide both techniques and complexity bounds for the different variants of the problem. Finally, we study the relationship between viewbased query containment and viewbased query rewriting.
LTL over description logic axioms
 In Proceedings of DL08, CEUR Workshop Proceedings. CEURWS.org
, 2008
"... In many applications of Description Logics (DLs) [7], such as the use of DLs as ontology languages or conceptual modeling languages, being able to represent dynamic aspects of the application domain would be quite useful. This is, for instance, the case if one wants to use DLs as conceptual modeling ..."
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Cited by 18 (3 self)
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In many applications of Description Logics (DLs) [7], such as the use of DLs as ontology languages or conceptual modeling languages, being able to represent dynamic aspects of the application domain would be quite useful. This is, for instance, the case if one wants to use DLs as conceptual modeling languages
Resets vs. Aborts in Linear Temporal Logic
, 2003
"... There has been a major emphasis recently in the semiconductor industry on designing industrialstrength property specification languages. Two major languages are ForSpec and Sugar 2.0, which are both extensions of Pnueli's LTL. Both ..."
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Cited by 11 (3 self)
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There has been a major emphasis recently in the semiconductor industry on designing industrialstrength property specification languages. Two major languages are ForSpec and Sugar 2.0, which are both extensions of Pnueli's LTL. Both
The Complexity of ResourceBounded FirstOrder Classical Logic
 11th Symposium on Theoretical Aspects of Computer Science
, 1994
"... . We give a finer analysis of the difficulty of proof search in classical firstorder logic, other than just saying that it is undecidable. To do this, we identify several measures of difficulty of theorems, which we use as resource bounds to prune infinite proof search trees. In classical firstord ..."
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Cited by 8 (1 self)
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. We give a finer analysis of the difficulty of proof search in classical firstorder logic, other than just saying that it is undecidable. To do this, we identify several measures of difficulty of theorems, which we use as resource bounds to prune infinite proof search trees. In classical firstorder logic without interpreted symbols, we prove that for all these measures, the search for a proof of bounded difficulty (i.e, for a simple proof) is \Sigma p 2 complete. We also show that the same problem when the initial formula is a set of Horn clauses is only NPcomplete, and examine the case of firstorder logic modulo an equational theory. These results allow us not only to give estimations of the inherent difficulty of automated theorem proving problems, but to gain some insight into the computational relevance of several automated theorem proving methods. Topics: computational complexity, logics, computational issues in AI (automated theorem proving). 1 Introduction Firstorder ...
Complexity of Decentralized Control: Special Cases
"... The worstcase complexity of general decentralized POMDPs, which are equivalent to partially observable stochastic games (POSGs) is very high, both for the cooperative and competitive cases. Some reductions in complexity have been achieved by exploiting independence relations in some models. We show ..."
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Cited by 8 (0 self)
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The worstcase complexity of general decentralized POMDPs, which are equivalent to partially observable stochastic games (POSGs) is very high, both for the cooperative and competitive cases. Some reductions in complexity have been achieved by exploiting independence relations in some models. We show that these results are somewhat limited: when these independence assumptions are relaxed in very small ways, complexity returns to that of the general case. 1
Tiling groups for Wang tiles
 proceedings of the 13 th annual ACMSIAM Symposium On Discrete Algorithms (SODA) SIAM eds
"... We apply tiling groups and height functions to tilings of regions in the plane by Wang tiles, which are squares with colored boundaries where the colors of shared edges must match. We define a set of tiles as unambiguous if it contains all tiles equivalent to the identity in its tiling group. For al ..."
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Cited by 6 (3 self)
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We apply tiling groups and height functions to tilings of regions in the plane by Wang tiles, which are squares with colored boundaries where the colors of shared edges must match. We define a set of tiles as unambiguous if it contains all tiles equivalent to the identity in its tiling group. For all but one set of unambiguous tiles with two colors, we give efficient algorithms that tell whether a given region with colored boundary is tileable, show how to sample random tilings, and how to calculate the number of local moves or “flips ” required to transform one tiling into another. We also analyze the lattice structure of the set of tilings, and study several examples with three and four colors as well. 1
Aborts vs resets in linear temporal logic
 In Proc. 9th International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS
, 2003
"... Abstract. There has been a major emphasis recently in the semiconductor industry on designing industrialstrength property specification languages (PSLs). Two major languages are ForSpec and Sugar 2.0, which are both extensions of Pnueli’s LTL. Both ForSpec and Sugar 2.0 directly support reset/abort ..."
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Cited by 4 (1 self)
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Abstract. There has been a major emphasis recently in the semiconductor industry on designing industrialstrength property specification languages (PSLs). Two major languages are ForSpec and Sugar 2.0, which are both extensions of Pnueli’s LTL. Both ForSpec and Sugar 2.0 directly support reset/abort signals, in which a check for a property ψ may be terminated and declared successful by an reset/abort signal, provided the check has not yet failed. ForSpec and Sugar 2.0, however, differ in their definition of failure. The definition of failure in ForSpec is syntactic, while the definition in Sugar 2.0 is semantic. In this work we examine the implications of this distinction between the two approaches, which we refer to as the reset approach (for ForSpec) and the abort approach (for Sugar 2.0). In order to focus on the reset/abort issue, we do not consider the full languages, which are quite rich, but rather the extensions of LTL with the reset/abort constructs. We show that the distinction between syntactic and semantic failure has a dramatic impact on the complexity of using the language in a modelchecking tool. We prove that ResetLTL enjoys the “fastcompilation property”: there is a linear translation of ResetLTL formulas into alternating Büchi automata, which implies a linear translation of ResetLTL formulas into a symbolic representation of nondeterministic Büchi automata. In contrast, the translation of AbortLTL formulas into alternating Büchi automata is nonelementary (i.e., cannot be bounded by a stack of exponentials of a bounded height); each abort yields an exponential blowup in the translation. This complexity bounds also apply to model checking; model checking ResetLTL formulas is exponential in the size of the property, while model checking AbortLTL formulas is nonelementary in the size of the property (the same bounds apply to satisfiability checking). 1