Reasoning about knowledge
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Expressive Equivalence of Least and Inflationary Fixed-Point Logic
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Monadic Second Order Logic on Tree-Like Structures
STACS '96 Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science
Will Deflation Lead to Depletion? On Non-Monotone Fixed Point Inductions
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Word problems requiring exponential time(Preliminary Report)
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Automata logics, and infinite games: a guide to current research
Automata logics, and infinite games: a guide to current research
Inflationary fixed points in modal logic
ACM Transactions on Computational Logic (TOCL)
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We define a new class of games, called backtracking games. Backtracking games are essentially parity games with an additional rule allowing players, under certain conditions, to return to an earlier position in the play and revise a choice or to force a countback of the number of moves. This new feature makes backtracking games more powerful than parity games. As a consequence, winning strategies become more complex objects and computationally harder. The corresponding increase in expressiveness allows us to use backtracking games as model-checking games for inflationary fixed-point logics such as IFP or MIC. We identify a natural subclass of backtracking games, the simple games, and show that these are the "right" model-checking games for IFP by (a) giving a translation of formulae ϕ and structures U into simple games such that U = φ if, and only if, Player 0 wins the corresponding game and (b) showing that the winner of simple backtracking games can again be defined in IFP.