Deterministic Generators and Games for LTL Fragments

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Departmental Papers (CIS)
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CPS Theory
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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 omega-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(dlog n)-space procedure to solve a Büchi game on a graph with n vertices and longest distance d. Then, for the LTL fragment with only 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 provide 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. Finally, we show tightness of the double-exponential bound on the size as well as the longest distance for deterministic generators for LTL even in the absence of next and until modalities.

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2001-06-16
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Departmental Papers (CIS)
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2023-05-16T21:38:17.000
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Copyright 2001 IEEE. Reprinted from Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science, 2001, pages 291-300. Publisher URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isNumber=20180&page=1 This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
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