J.R. Buchi and L.H. Landweber. Solving sequential conditions by finite-state strategies. Transactions of the AMS, 138:295--311, 1969.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....must find a winning player 2 strategy for this game structure. Let be the set of states where player 2 is non blocked. The game can then be cast as a safety game: player 2 must never leave ( #, The solution to this safety game is entirely classical [10, 11]. To solve the games, for a set of states we define the set 87 :9 of controllable predecessors of as the set consisting of all states where there is # ; In formulas, 8 ....

....2 is winning if, for all player 1 strategies , there is 2358 such that . Again, a protocol converter corresponds to a winning strategy. Games with such fairness conditions and winning conditions are examples of games with regular winning conditions [11]. Such games can be solved by the methods of [11, 14, 15, 12] a winning strategy can be easily derived from a game solution. We note that, when fairness is present, the winning strategy may require memory. Nevertheless, the protocol converter can again be synthesized as an automaton, since the ....

[Article contains additional citation context not shown here]

J. Buchi and L. Landweber, "Solving sequential conditions by finite-state strategies," Trans. Amer. Math. Soc., vol. 138, pp. 295--311, 1969.

.... and the creation of infinite state machines, based on the timed automata model, meeting temporal specifications [29, 34] A much earlier work by Buchi and Landweber investigates the conditions for a relation between input and output # sequences to be satisfiable by a finite state automaton [3]. 10.6 Abstract State Machines The description of computational processes as abstract state machines (ASMs) is similar to our model of dynamic computation as a relational structure that is updated sequentially. ASMs, previously called evolving algebras, are being used as an operational ....

Buchi, J. Richard, and Landweber, Lawrence H. Solving sequential conditions by finite-state strategies. Trans. Amer. Math. Soc. 138 (1969), 295--311.

....we must find a winning player 2 strategy for this game structure. Let # ######## # ## # # # ## ### ## ## be the set of states where player 2 is non blocked. The game can then be cast as a safety game: player 2 must never leave # ######## . The solution to this safety game is entirely classical [10, 11]. To solve the games, for a set of states # # # we define the set ###### # # # of controllable predecessors of # as the set consisting of all states # # # where there is ## # ## ### such that for all ## # #####, we have ### #### # # # # . In formulas, ###### # # ## # # #### # ######### # ## ....

....## for player 2 is winning if, for all player 1 strategies ## , there is # # ########## ## # ## # # such that # ## #. Again, a protocol converter corresponds to a winning strategy. Games with such fairness conditions and winning conditions are examples of games with # regular winning conditions [11]. Such games can be solved by the methods of [11, 14, 15, 12] a winning strategy can be easily derived from a game solution. We note that, when fairness is present, the winning strategy may require memory. Nevertheless, the protocol converter can again be synthesized as an automaton, since the ....

[Article contains additional citation context not shown here]

J. Buchi and L. Landweber, "Solving sequential conditions by finite-state strategies," Trans. Amer. Math. Soc., vol. 138, pp. 295--311, 1969.

....#, a WCET map w for #, and a bound k there is a scheduling strategy # such that all infinite traces of (#, w) that are outcomes of # are both time safe and k bounded. Two player safety games. Schedulability can be solved as a safety game on the configuration graph [1] A two player safety game [2] G = V, E, V 0 , U) consists of a finite set V of vertices, a relation E of edges, a set V 0 V of initial vertices, and a set U V of safe vertices. The vertices V are partitioned into V 1 and V 2 . The game is turn based and proceeds in rounds. For i = 1, 2, when the game is in v ....

J.R. Buchi and L.H. Landweber. Solving sequential conditions by finite-state strategies. Trans. AMS, 138:295--311, 1969.

.... or average reward that player 1 can obtain in such a game; a survey of algorithms for solving games with respect to such winning conditions is e.g. RF91, FV97] Here, we consider winning conditions consisting in regular automata acceptance conditions defined over the state space of the game [BL69, GH82, Tho95] Given a game with an regular winning condition and a starting state s, we study the maximal probability with which player 1 can ensure that the condition holds from s; we call this maximal probability the value of the game at s for player 1. The determinacy result of [Mar90] ....

....successor state. For any regular winning condition, the value of a deterministic turn based game at a state is either 0 or 1; moreover, player 1 can achieve this value by playing according to a deterministic strategy, that select a move based on the current state and on the history of the game [BL69, GH82] In contrast, the value of a concurrent game at a state may be strictly between 0 and 1; furthermore, achieving this value may require the use of randomized strategies, that select not a move, but a probability distribution over moves. To see this, consider the concurrent game MatchOneBit. ....

[Article contains additional citation context not shown here]

J.R. Buchi and L.H. Landweber. Solving sequential conditions by finite-state strategies. Trans. Amer. Math. Soc., 138:295--311, 1969.

....a = Pre 1 ( f(oe) Then poeq p a2A oe a q, because there is always at least one controlling action. If the game is at state (q; s) 2 poeq for a region oe 2 U , define f(q; s) fa 2 A j (q; s) 2 poe a qg. Unlike a control strategy for C Theta G, a control strategy for G may need memory [6, 16]. We can construct such a strategy f as follows. As the game goes on, the strategy f feeds the observables of the visited states to a copy of the Rabin chain automaton C, remembering the current state of the automaton. Upon reaching a state s, player 1 chooses an action in f(q; s) where q ....

J. Buchi and L. Landweber. Solving sequential conditions by finite-state strategies. Transactions of the AMS, 138:295--311, 1969.

....for certain inputs. For our games we provide two simple polynomial time algorithms for deciding update networks, partially based on the structural properties of the underlying graphs. We also note that several earlier papers have dealt with finite duration games on automata and graphs (e.g. see [3, 4]) 2 Update Games We now model a natural communication network problem. Suppose we have data stored on each node of a network and we want to continuously update all nodes with Update Games and Update Networks 3 2 3 4 5 6 W = 1, 3 , 2, 3, 4, 5 , 4, 5, 6 V = 1, 2, 3, 4, 5, 6 E = ....

R.J. Buchi and L.H Landweber. Solving sequential conditions by finite-state strategies. Trans. Amer. Math. Soc. 138 (1969), 295--311.

....to a sure win, i.e. L F A Gamma . A finite state winning strategy for the environment is defined similarly, but for obvious reasons we are not interested in those here. A classical theorem of Buchi and Landweber on regular infinite games states that Theorem16 (Reg. games are determined [BL69] If (I; O; Gamma ) is a regular game then one of the players has a finite state winning strategy. It can be decided effectively who has, and the finite state winning strategy can be constructed effectively. This result becomes helpful to synthesis of clocked controllers through the following ....

J. R. Buchi and L. H. Landweber. Solving sequential conditions by finitestate strategies. Trans. Amer. Math. Soc., 138:295--311, 1969.

....opponent can escape to other parts of the state space via discrete jumps. In dimensions even as low as three, these calculations can become infeasible. In the discrete domain, Church s classical synthesis problem was first solved by reduction to a zero sum, two person game over infinite strings [2]. Numerous researchers have studied solutions to the synthesis problem via translations to tree automata; a tree is accepted iff it corresponds to a winning strategy, e.g. 11, 10] For safety games, the game admits a particularly simple solution that consists of a fixpoint algorithm that ....

J. R. Buchi and L. H. Landweber. Solving sequential conditions by finite-state strategies. Transactions of the American Mathematical Society, 138:295--311, 1969.

....the game is infinite. When all of the processes and the specification can be modeled as finite automata on infinite words, or formulas from a logic interpreted over infinite words, the synthesis problem is decidable. The decision procedures consist of reductions to the Church solvability problem, [Chu63, BL69] which can be solved using automata on infinite trees [Rab72] Supported by NSF under grant MIP 8858807. 1 Our processes have three different types of variables: shared, read only, and distributed (variables that can be read by other processes but written only by one) We solve the particular ....

....(S) is in W . The Finite State Case If the problem is finite state (the behaviors of the processes and the specification can be represented as regular sets) the read write game is decidable. This result follows almost immediately from the decidability of the Church Buchi solvability problem, [BL69, Rab72]. We assume that processes and specifications are related as Buchi automata [Buc62] We use the fact that regular languages are closed under the operations of complementation, union, and (therefore) intersection. Theorem 1 Let A be a nondeterministic Buchi automaton (NBA) defining Spec, a set ....

J. R. Buchi and L. H. Landweber, "Solving sequential conditions by finite-state strategies", Transactions of the American Mathematical Society, 138, April, 1969, pp. 295--311.

....problem for # is to find a finite state input output automaton (transducer) such that the function F computable by the automata satisfies #X. #(X, F (X) The uniformization problem for the monadic second order theory of order of the structure # was solved positively by Buchi and Landweber [2]. We check whether these classical results can be extended to continuous time. In [11] automata that accept finitely variable languages were defined. It was announced there that a finitely variability language is definable in monadic logic i# it is accepted by a finite state automata. Here we show ....

....Th # # # X# # Y .# # ( # X , # Y ) Here # means there is a unique . Hence, # # defines the graph of a function which lies inside the set definable by #. The uniformization problem for the monadic second order theory of order of the structure # was solved positively by Buchi and Landweber [2]. Below we show that the uniformization fails in both the finitely variable and the right continuous signal structures. First observe that if x = x # # for every order preserving bijection # on R #0 , then x is constant on the positive reals. Recall that the languages definable in Rsig and in ....

J. R. Buchi and L. H. Landweber. Solving sequential conditions by finite-state strategies. Transactions of the American Mathematical Society, vol 138 (1969), pp. 295-311.

....and the definition of parallel composition plays a central role in this study, or (2) the multi step control problem (for invariance or even more general, regular objectives) assuming to be given a solution to the single step problem. While (2) has been researched extensively in the literature [BL69,GH82,RW87,EJ91,McN93,TW94,Tho95], it is (1) we focus on in this paper. We assume that the plant M is specified in a compact form, by a transition predicate on boolean variables, so that the state space of M is exponentially larger than the description of M , which is the input to the control problem. For solving the multi step ....

J.R. Buchi and L.H. Landweber. Solving sequential conditions by finite-state strategies. Trans. Amer. Math. Soc., 138:295--311, 1969.

....Given a plant P , a desired behavior K, the problem is to construct a supervisor S, if it exists, such that its interaction with the plant P will always result in a word w from K. The classical approach to the solution of the above problems was initiated and developed in papers by [Buc62, BL69] It is based on paradigms of automata theory, especially finite state machines and languages and results in simply and clearly formulated models and solutions. This has theoretical advantages, but for practical purposes, due to the exponential complexity of the algorithm for the supervisor ....

J. R. Buchi and L. H. Landweber. Solving sequential conditions by finite state strategies. Transactions of American Mathematical Society, 1969.

....concurrent games generalize several models, including Markov chains, Markov decision processes, deterministic as well as probabilistic turn based games, and deterministic concurrent games. Previously, solutions to games have been known only for (1) all varieties of deterministic turn based games [BL69, GH82, EJ91, Tho95] 2) concurrent Rabin chain games, played with deterministic strategies (these games can be solved like turn based games) AHK97] and (3) concurrent reachability games, played with randomized strategies [dAHK98] We note that already the case for probabilistic turn based ....

....m is the number of pairs in the Rabin chain condition. While this complexity is in line with the solution for turn based Rabin chain games [EJ91] our algorithms are considerably more involved than those for turn based games. This has several reasons. First, while turn based games are determined [BL69] in every state, either player 1 has a winning strategy, which guarantees a win no matter what player 2 does, or 2 player 2 has a spoiling strategy, which guarantees that the winning condition is violated no matter what player 1 does) concurrent games are generally not determined. For ....

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J.R. Buchi and L.H. Landweber. Solving sequential conditions by finite-state strategies. Trans. Amer. Math. Soc., 138:295--311, 1969.

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J.R. Buchi and L.H. Landweber. Solving sequential conditions by finite-state strategies. Transactions of the AMS, 138:295--311, 1969.

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J.R. Buchi and L.H. Landweber. Solving sequential conditions by finitestate strategies. Transactions of the AMS, 138:295--311, 1969. 27

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J. Buchi and L. Landweber. Solving sequential conditions by finite-state strategies. Transactions of the American Mathematical Society, 138:295--311, 1969.

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J.R. Buchi and L.H. Landweber. Solving sequential conditions by finite-state strategies. Trans. Amer. Math. Soc., 138:295--311, 1969.

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J. R. Buchi and L. H. Landweber. Solving sequential conditions by finite-state strategies. Transactions of the American Mathematical Society, 138:295-311, 1969.

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J.R. Buchi and L.H. Landweber. Solving sequential conditions by finite-state strategies. Trans. Amer. Math. Soc., 138:295--311, 1969.

No context found.

J. Buchi and L. Landweber. Solving sequential conditions by finite-state strategies. Transactions of the American Mathematical Society, 138:295--311, 1969.

No context found.

J.R. Buchi and L.H. Landweber. Solving sequential conditions by finite-state strategies. Trans. Amer. Math. Soc., 138:295--311, 1969.

No context found.

J.R. Buchi and L.H. Landweber. Solving sequential conditions by finite-state strategies. Transactions of the AMS, 138:295--311, 1969.

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J. R. Buchi, L.H. Landweber. Solving Sequential Conditions by Finite State Strategies. Trans. Amer. Math. Soc. 138, p.295-311, 1969.

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J. R. Buchi and L. H. Landweber. Solving sequential conditions by finite-state strategies. Trans. Amer. Math. Soc., 138:295--311, 1969.

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