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The complexity of one-agent Refinement Modal Logic

by Laura Bozzelli, Hans Van Ditmarsch, Sophie Pinchinat
"... Abstract. We investigate the complexity of satisfiability for one-agent Refinement Modal Logic (RML), a known extension of basic modal logic (ML) obtained by adding refinement quantifiers on structures. It is known that RML has the same expressiveness as ML, but the translation of RML into ML is of ..."
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-satisfiability is complete for the complexity class AEXPpol, i.e., the class of problems solvable by alternating Turing machines running in single exponential time but only with a polynomial number of alternations (note that NEXPTIME ⊆ AEXPpol ⊆ EXPSPACE). 1

An EXPSPACE Tableau-based Algorithm for SHOIQ

by Chan Le Duc, Myriam Lamolle, Olivier Curé
"... Abstract. In this paper, we propose an EXPSPACE tableau-based algorithm for SHOIQ. The construction of this algorithm is founded on the standard tableaubased method for SHOIQ and the technique used for designing a NEXPTIME algorithm for the two-variable fragment of first-order logic with counting qu ..."
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Abstract. In this paper, we propose an EXPSPACE tableau-based algorithm for SHOIQ. The construction of this algorithm is founded on the standard tableaubased method for SHOIQ and the technique used for designing a NEXPTIME algorithm for the two-variable fragment of first-order logic with counting

An EXPSPACE Tableaux-Based Algorithm for SHOIQ

by Chan Le Duc, Myriam Lamolle, Olivier Curé , 2013
"... Abstract. In this paper, we propose an EXPSPACE tableaux-based algorithm for SHOIQ. The construction of this algorithm is founded on the standard tableauxbased method for SHOIQ and the technique used for designing a NEXPTIME algorithm for the two-variable fragment of first-order logic with counting ..."
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Abstract. In this paper, we propose an EXPSPACE tableaux-based algorithm for SHOIQ. The construction of this algorithm is founded on the standard tableauxbased method for SHOIQ and the technique used for designing a NEXPTIME algorithm for the two-variable fragment of first-order logic with counting

1Distributed Synthesis for LTL Fragments

by Krishnendu Chatterjee, Thomas A. Henzinger, Jan Otop, Andreas Pavlogiannis
"... Abstract—We consider the distributed synthesis problem for temporal logic specifications. Traditionally, the problem has been studied for LTL, and the previous results show that the problem is decidable iff there is no information fork in the architecture. We consider the problem for fragments of LT ..."
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establish decidability (in EXPSPACE) for star architectures where the processes receive disjoint inputs, whereas we establish undecidability for architectures containing an information fork-meet structure. (3) Finally, we consider LTL without the next operator, and establish decidability (NEXPTIME

Semantic evaluation, intersection types and complexity of simply typed lambda calculus

by Kazushige Terui - Schloss Dagstuhl - LeibnizZentrum fuer Informatik , 2012
"... Consider the following problem: given a simply typed lambda term of Boolean type and of order r, does it normalize to “true”? A related problem is: given a term M of word type and of order r together with a finite automaton D, does D accept the word represented by the normal form of M? We prove that ..."
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that these problems are n-EXPTIME complete for r = 2n + 2, and n-EXPSPACE complete for r = 2n + 3. While the hardness part is relatively easy, the membership part is not so obvious; in particular, simply applying β reduction does not work. Some preceding works employ semantic evaluation in the category of sets

Tight Bounds for HTN planning with Task Insertion

by Ron Alford, Pascal Bercher, David W. Aha
"... Hierarchical Task Network (HTN) planning with Task Insertion (TIHTN planning) is a formalism that hybridizes classical planning with HTN plan-ning by allowing the insertion of operators from outside the method hierarchy. This additional capa-bility has some practical benefits, such as allowing more ..."
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applied in practice, its theo-retical properties have not been studied in detail, yet – only EXPSPACE membership is known so far. We lower that bound proving NEXPTIME-completeness and further prove tight complexity bounds along two axes: whether variables are al-lowed in method and action schemas

On first-order fragments for Mazurkiewicz traces

by Volker Diekert, Martin Horsch, Manfred Kufleitner
"... Abstract Mazurkiewicz traces form a model for concurrency. Temporal logic and first-order logic are important tools in order to deal with the abstract behavior of such systems. Since typical properties can be described by rather simple logical formulas one is interested in logical fragments. One foc ..."
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prove an nexptime upper bound, whereas the corresponding problem for partial orders leads to expspace. Furthermore, we give several separation results for the alternation hierarchy for first-order logic. It turns out that even for those levels at which one can express the partial order relation in terms
Results 1 - 7 of 7