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Rectangular Hybrid Games
 In CONCUR 99, LNCS 1664
, 1999
"... In order to study control problems for hybrid systems, we generalize hybrid automata to hybrid games  say, controller vs. plant. If we specify the continuous dynamics by constant lower and upper bounds, we obtain rectangular games. We show that for rectangular games with objectives expressed in Lt ..."
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Cited by 30 (4 self)
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In order to study control problems for hybrid systems, we generalize hybrid automata to hybrid games  say, controller vs. plant. If we specify the continuous dynamics by constant lower and upper bounds, we obtain rectangular games. We show that for rectangular games with objectives expressed in Ltl (linear temporal logic), the winning states for each player can be computed, and winning strategies can be synthesized. Our result is sharp, as already reachability is undecidable for generalizations of rectangular systems, and optimal  singly exponential in the size of the game structure and doubly exponential in the size of the Ltl objective. Our proof systematically generalizes the theory of hybrid systems from automata (singleplayer structures) [9] to games (multiplayer structures): we show that the successively more general infinitestate classes of timed, 2d rectangular, and rectangular games induce successively weaker, but still finite, quotient structures called game bisimilarity, game similarity, and game trace equivalence. These quotients can be used, in particular, to solve the Ltl control problem.
Guarded Quantification in Least Fixed Point Logic
, 2002
"... We develop a variant of Least Fixed Point logic based on First Order logic with a relaxed version of guarded quantification. We develop a Game Theoretic Semantics of this logic, and find that under reasonable conditions, guarding quantification does not reduce the expressibility of Least Fixed Point ..."
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Cited by 2 (1 self)
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We develop a variant of Least Fixed Point logic based on First Order logic with a relaxed version of guarded quantification. We develop a Game Theoretic Semantics of this logic, and find that under reasonable conditions, guarding quantification does not reduce the expressibility of Least Fixed Point logic. But guarding quantification increases worstcase time complexity.
On the Universal and Existential Fragments of the µCalculus
, 2003
"... One source of complexity in the µcalculus is its ability to specify an unbounded number of switches between universal (AX) and existential (EX) branching modes. We therefore study the problems of satis ability, validity, model checking, and implication for the universal and existential fragmen ..."
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Cited by 1 (0 self)
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One source of complexity in the µcalculus is its ability to specify an unbounded number of switches between universal (AX) and existential (EX) branching modes. We therefore study the problems of satis ability, validity, model checking, and implication for the universal and existential fragments of the µcalculus, in which only one branching mode is allowed. The universal fragment is rich enough to express most specifications of interest, and therefore improved algorithms are of practical importance. We show that while the satis ability and validity problems become indeed simpler for the existential and universal fragments, this is, unfortunately, not the case for model checking and implication.