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Deterministic Generators and Games for Ltl RAJEEV ALUR
 

Summary: Deterministic Generators and Games for Ltl
Fragments
RAJEEV ALUR
University of Pennsylvania
and
SALVATORE LA TORRE
University of Pennsylvania and Universit`a degli Studi di Salerno
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 -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 Bšuchi 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

  

Source: Alur, Rajeev - Department of Computer and Information Science, University of Pennsylvania

 

Collections: Computer Technologies and Information Sciences