Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Deterministic generators and games for Ltl fragments

Deterministic generators and games for Ltl fragments 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 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 O ( d log n )-space procedure to solve a Büchi game on a graph with n vertices and longest distance 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 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 next and until modalities. Finally, we identify a class of deterministic Büchi automata corresponding to a fragment of Ltl with restricted use of always and until modalities, for which deciding games is Pspace-complete. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

Deterministic generators and games for Ltl fragments

Loading next page...
 
/lp/association-for-computing-machinery/deterministic-generators-and-games-for-ltl-fragments-mvmPZFzDVp

References (4)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2004 by ACM Inc.
ISSN
1529-3785
DOI
10.1145/963927.963928
Publisher site
See Article on Publisher Site

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 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 O ( d log n )-space procedure to solve a Büchi game on a graph with n vertices and longest distance 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 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 next and until modalities. Finally, we identify a class of deterministic Büchi automata corresponding to a fragment of Ltl with restricted use of always and until modalities, for which deciding games is Pspace-complete.

Journal

ACM Transactions on Computational Logic (TOCL)Association for Computing Machinery

Published: Jan 1, 2004

There are no references for this article.