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Deterministic generators and games for Ltl fragments

Content Provider	ACM Digital Library
Author	Alur, Rajeev La torre, Salvatore
Copyright Year	2004
Abstract	Deciding infinite two-player games on finite graphs with the winning condition specified by a linear temporal logic (Ltl) formula, is known to be 2Exptime-complete. In this paper, we identify Ltl fragments of lower complexity. Solving Ltl games typically involves a doubly exponential translation from Ltl formulas to $\textit{deterministic}$ ω-automata. First, we show that the longest distance (length of the longest simple path) of the generator is also an important parameter, by giving an $\textit{O}(\textit{d}$ log $\textit{n})-space$ procedure to solve a Büchi game on a graph with $\textit{n}$ vertices and longest distance $\textit{d}.$ Then, for the Ltl fragment of the Boolean combinations of formulas obtained only by eventualities and conjunctions, we provide a translation to deterministic generators of exponential size and linear longest distance, show both of these bounds to be optimal, and prove the corresponding games to be Pspace-complete. Introducing $\textit{next}$ modalities in this fragment, we give a translation to deterministic generators still of exponential size but also with exponential longest distance, show both of these bounds to be optimal, and prove the corresponding games to be Exptime-complete. For the fragment resulting by further adding disjunctions, we provide a translation to deterministic generators of doubly exponential size and exponential longest distance, show both of these bounds to be optimal, and prove the corresponding games to be Expspace. We also show tightness of the double exponential bound on the size as well as the longest distance for deterministic generators of Ltl formulas without $\textit{next}$ and $\textit{until}$ modalities. Finally, we identify a class of deterministic Büchi automata corresponding to a fragment of Ltl with restricted use of $\textit{always}$ and $\textit{until}$ modalities, for which deciding games is Pspace-complete.
Starting Page	1
Ending Page	25
Page Count	25
File Format	PDF
ISSN	15293785
e-ISSN	1557945X
DOI	10.1145/963927.963928
Volume Number	5
Issue Number	1
Journal	ACM Transactions on Computational Logic (TOCL)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2004-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Automata Games Temporal Logic
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Logic Computational Mathematics Computer Science

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