844 research outputs found
Degrees of Lookahead in Regular Infinite Games
We study variants of regular infinite games where the strict alternation of
moves between the two players is subject to modifications. The second player
may postpone a move for a finite number of steps, or, in other words, exploit
in his strategy some lookahead on the moves of the opponent. This captures
situations in distributed systems, e.g. when buffers are present in
communication or when signal transmission between components is deferred. We
distinguish strategies with different degrees of lookahead, among them being
the continuous and the bounded lookahead strategies. In the first case the
lookahead is of finite possibly unbounded size, whereas in the second case it
is of bounded size. We show that for regular infinite games the solvability by
continuous strategies is decidable, and that a continuous strategy can always
be reduced to one of bounded lookahead. Moreover, this lookahead is at most
doubly exponential in the size of a given parity automaton recognizing the
winning condition. We also show that the result fails for non-regular
gamesxwhere the winning condition is given by a context-free omega-language.Comment: LMCS submissio
無限ゲームと様相μ計算の部分体系についてのオートマトン理論的研究
要約のみTohoku University田中一之課
Model-Checking the Higher-Dimensional Modal mu-Calculus
The higher-dimensional modal mu-calculus is an extension of the mu-calculus
in which formulas are interpreted in tuples of states of a labeled transition
system. Every property that can be expressed in this logic can be checked in
polynomial time, and conversely every polynomial-time decidable problem that
has a bisimulation-invariant encoding into labeled transition systems can also
be defined in the higher-dimensional modal mu-calculus. We exemplify the latter
connection by giving several examples of decision problems which reduce to
model checking of the higher-dimensional modal mu-calculus for some fixed
formulas. This way generic model checking algorithms for the logic can then be
used via partial evaluation in order to obtain algorithms for theses problems
which may benefit from improvements that are well-established in the field of
program verification, namely on-the-fly and symbolic techniques. The aim of
this work is to extend such techniques to other fields as well, here
exemplarily done for process equivalences, automata theory, parsing, string
problems, and games.Comment: In Proceedings FICS 2012, arXiv:1202.317
Collapsible Pushdown Parity Games
International audienceThis paper studies a large class of two-player perfect-information turn-based parity games on infinite graphs, namely those generated by collapsible pushdown automata. The main motivation for studying these games comes from the connections from collapsible pushdown automata and higher-order recursion schemes, both models being equi-expressive for generating infinite trees. Our main result is to establish the decidability of such games and to provide an effective representation of the winning region as well as of a winning strategy. Thus, the results obtained here provide all necessary tools for an in-depth study of logical properties of trees generated by collapsible pushdown automata/recursion schemes
One-Counter Stochastic Games
We study the computational complexity of basic decision problems for
one-counter simple stochastic games (OC-SSGs), under various objectives.
OC-SSGs are 2-player turn-based stochastic games played on the transition graph
of classic one-counter automata. We study primarily the termination objective,
where the goal of one player is to maximize the probability of reaching counter
value 0, while the other player wishes to avoid this. Partly motivated by the
goal of understanding termination objectives, we also study certain "limit" and
"long run average" reward objectives that are closely related to some
well-studied objectives for stochastic games with rewards. Examples of problems
we address include: does player 1 have a strategy to ensure that the counter
eventually hits 0, i.e., terminates, almost surely, regardless of what player 2
does? Or that the liminf (or limsup) counter value equals infinity with a
desired probability? Or that the long run average reward is >0 with desired
probability? We show that the qualitative termination problem for OC-SSGs is in
NP intersection coNP, and is in P-time for 1-player OC-SSGs, or equivalently
for one-counter Markov Decision Processes (OC-MDPs). Moreover, we show that
quantitative limit problems for OC-SSGs are in NP intersection coNP, and are in
P-time for 1-player OC-MDPs. Both qualitative limit problems and qualitative
termination problems for OC-SSGs are already at least as hard as Condon's
quantitative decision problem for finite-state SSGs.Comment: 20 pages, 1 figure. This is a full version of a paper accepted for
publication in proceedings of FSTTCS 201
Collapsible Pushdown Automata and Recursion Schemes
International audienceWe consider recursion schemes (not assumed to be homogeneously typed, and hence not necessarily safe) and use them as generators of (possibly infinite) ranked trees. A recursion scheme is essentially a finite typed {deterministic term} rewriting system that generates, when one applies the rewriting rules ad infinitum, an infinite tree, called its value tree. A fundamental question is to provide an equivalent description of the trees generated by recursion schemes by a class of machines. In this paper we answer this open question by introducing collapsible pushdown automata (CPDA), which are an extension of deterministic (higher-order) pushdown automata. A CPDA generates a tree as follows. One considers its transition graph, unfolds it and contracts its silent transitions, which leads to an infinite tree which is finally node labelled thanks to a map from the set of control states of the CPDA to a ranked alphabet. Our contribution is to prove that these two models, higher-order recursion schemes and collapsible pushdown automata, are equi-expressive for generating infinite ranked trees. This is achieved by giving an effective transformations in both directions
Three notes on the complexity of model checking fixpoint logic with chop
This paper analyses the complexity of model checking fixpoint logic with Chop – an extension of the
modal μ-calculus with a sequential composition operator. It uses two known game-based characterisations
to derive the following results: the combined model checking complexity as well as the data complexity
of FLC are EXPTIME-complete. This is already the case for its alternation-free fragment. The expression
complexity of FLC is trivially P-hard and limited from above by the complexity of solving a
parity game, i.e. in UP ∩ co-UP. For any fragment of fixed alternation depth, in particular alternation-
free formulas it is P-complete
Playing with Trees and Logic
This document proposes an overview of my research sinc
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