Parameterized modal satisfiability

Authors:
Antonis Achilleos;Michael Lampis;Valia Mitsou
Affiliations:
Computer Science Department, Graduate Center, City University of New York, New York, NY;Computer Science Department, Graduate Center, City University of New York, New York, NY;Computer Science Department, Graduate Center, City University of New York, New York, NY
Venue:
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Year:
2010

Citing 8
Cited 2

The monadic second-order logic of graphs. I. recognizable sets of finite graphs

Information and Computation
A guide to completeness and complexity for modal logics of knowledge and belief

Artificial Intelligence
Reasoning about knowledge

Reasoning about knowledge
The effect of bounding the number of primitive propositions and the depth of nesting on the complexity of modal logic

Artificial Intelligence
The Complexity of First-Order and Monadic Second-Order Logic Revisited

LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Exact algorithms for NP-hard problems: a survey

Combinatorial optimization - Eureka, you shrink!
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)

Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Handbook of Modal Logic, Volume 3 (Studies in Logic and Practical Reasoning)

Handbook of Modal Logic, Volume 3 (Studies in Logic and Practical Reasoning)

Does treewidth help in modal satisfiability?

MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Does Treewidth Help in Modal Satisfiability?

ACM Transactions on Computational Logic (TOCL)

Quantified Score

Hi-index	0.00

Visualization

Abstract

We investigate the parameterized computational complexity of the satisfiability problem for modal logic and attempt to pinpoint relevant structural parameters which cause the problem's combinatorial explosion, beyond the number of propositional variables v. To this end we study the modality depth, a natural measure which has appeared in the literature, and show that, even though modal satisfiability parameterized by v and the modality depth is FPT, the running time's dependence on the parameters is a tower of exponentials (unless P=NP). To overcome this limitation we propose possible alternative parameters, namely diamond dimension and modal width. We show fixed-parameter tractability results using these measures where the exponential dependence on the parameters is much milder (doubly and singly exponential respectively) than in the case of modality depth thus leading to FPT algorithms for modal satisfiability with much more reasonable running times. We also give lower bound arguments which prove that our algorithms cannot be improved significantly unless the Exponential Time Hypothesis fails.