2,125 research outputs found
Synthesis of Finite-state and Definable Winning Strategies
Church\u27s Problem asks for the construction of a procedure which,
given a logical specification on sequence pairs, realizes
for any input sequence an output sequence such that
satisfies . McNaughton reduced Church\u27s Problem to a problem about two-player-games.
B"uchi and Landweber gave a solution for
Monadic Second-Order Logic of Order () specifications in terms of finite-state strategies.
We consider two natural generalizations of the Church problem to
countable ordinals: the first deals with finite-state strategies;
the second deals with -definable strategies. We investigate
games of arbitrary countable length and prove the computability of
these generalizations of Church\u27s problem
The Church Synthesis Problem with Parameters
For a two-variable formula ψ(X,Y) of Monadic Logic of Order (MLO) the
Church Synthesis Problem concerns the existence and construction of an operator
Y=F(X) such that ψ(X,F(X)) is universally valid over Nat.
B\"{u}chi and Landweber proved that the Church synthesis problem is
decidable; moreover, they showed that if there is an operator F that solves the
Church Synthesis Problem, then it can also be solved by an operator defined by
a finite state automaton or equivalently by an MLO formula. We investigate a
parameterized version of the Church synthesis problem. In this version ψ
might contain as a parameter a unary predicate P. We show that the Church
synthesis problem for P is computable if and only if the monadic theory of
is decidable. We prove that the B\"{u}chi-Landweber theorem can be
extended only to ultimately periodic parameters. However, the MLO-definability
part of the B\"{u}chi-Landweber theorem holds for the parameterized version of
the Church synthesis problem
Playing Games in the Baire Space
We solve a generalized version of Church's Synthesis Problem where a play is
given by a sequence of natural numbers rather than a sequence of bits; so a
play is an element of the Baire space rather than of the Cantor space. Two
players Input and Output choose natural numbers in alternation to generate a
play. We present a natural model of automata ("N-memory automata") equipped
with the parity acceptance condition, and we introduce also the corresponding
model of "N-memory transducers". We show that solvability of games specified by
N-memory automata (i.e., existence of a winning strategy for player Output) is
decidable, and that in this case an N-memory transducer can be constructed that
implements a winning strategy for player Output.Comment: In Proceedings Cassting'16/SynCoP'16, arXiv:1608.0017
O-Minimal Hybrid Reachability Games
In this paper, we consider reachability games over general hybrid systems,
and distinguish between two possible observation frameworks for those games:
either the precise dynamics of the system is seen by the players (this is the
perfect observation framework), or only the starting point and the delays are
known by the players (this is the partial observation framework). In the first
more classical framework, we show that time-abstract bisimulation is not
adequate for solving this problem, although it is sufficient in the case of
timed automata . That is why we consider an other equivalence, namely the
suffix equivalence based on the encoding of trajectories through words. We show
that this suffix equivalence is in general a correct abstraction for games. We
apply this result to o-minimal hybrid systems, and get decidability and
computability results in this framework. For the second framework which assumes
a partial observation of the dynamics of the system, we propose another
abstraction, called the superword encoding, which is suitable to solve the
games under that assumption. In that framework, we also provide decidability
and computability results
The Church Problem for Countable Ordinals
A fundamental theorem of Buchi and Landweber shows that the Church synthesis
problem is computable. Buchi and Landweber reduced the Church Problem to
problems about ω-games and used the determinacy of such games as one of
the main tools to show its computability. We consider a natural generalization
of the Church problem to countable ordinals and investigate games of arbitrary
countable length. We prove that determinacy and decidability parts of the
Bu}chi and Landweber theorem hold for all countable ordinals and that its full
extension holds for all ordinals < \omega\^\omega
Tree games with regular objectives
We study tree games developed recently by Matteo Mio as a game interpretation
of the probabilistic -calculus. With expressive power comes complexity.
Mio showed that tree games are able to encode Blackwell games and,
consequently, are not determined under deterministic strategies.
We show that non-stochastic tree games with objectives recognisable by
so-called game automata are determined under deterministic, finite memory
strategies. Moreover, we give an elementary algorithmic procedure which, for an
arbitrary regular language L and a finite non-stochastic tree game with a
winning objective L decides if the game is determined under deterministic
strategies.Comment: In Proceedings GandALF 2014, arXiv:1408.556
Formats of Winning Strategies for Six Types of Pushdown Games
The solution of parity games over pushdown graphs (Walukiewicz '96) was the
first step towards an effective theory of infinite-state games. It was shown
that winning strategies for pushdown games can be implemented again as pushdown
automata. We continue this study and investigate the connection between game
presentations and winning strategies in altogether six cases of game arenas,
among them realtime pushdown systems, visibly pushdown systems, and counter
systems. In four cases we show by a uniform proof method that we obtain
strategies implementable by the same type of pushdown machine as given in the
game arena. We prove that for the two remaining cases this correspondence
fails. In the conclusion we address the question of an abstract criterion that
explains the results
Synthesis of Deterministic Top-down Tree Transducers from Automatic Tree Relations
We consider the synthesis of deterministic tree transducers from automaton
definable specifications, given as binary relations, over finite trees. We
consider the case of specifications that are deterministic top-down tree
automatic, meaning the specification is recognizable by a deterministic
top-down tree automaton that reads the two given trees synchronously in
parallel. In this setting we study tree transducers that are allowed to have
either bounded delay or arbitrary delay. Delay is caused whenever the
transducer reads a symbol from the input tree but does not produce output. We
provide decision procedures for both bounded and arbitrary delay that yield
deterministic top-down tree transducers which realize the specification for
valid input trees. Similar to the case of relations over words, we use
two-player games to obtain our results.Comment: In Proceedings GandALF 2014, arXiv:1408.556
Uniform Strategies
We consider turn-based game arenas for which we investigate uniformity
properties of strategies. These properties involve bundles of plays, that arise
from some semantical motive. Typically, we can represent constraints on allowed
strategies, such as being observation-based. We propose a formal language to
specify uniformity properties and demonstrate its relevance by rephrasing
various known problems from the literature. Note that the ability to correlate
different plays cannot be achieved by any branching-time logic if not equipped
with an additional modality, so-called R in this contribution. We also study an
automated procedure to synthesize strategies subject to a uniformity property,
which strictly extends existing results based on, say standard temporal logics.
We exhibit a generic solution for the synthesis problem provided the bundles of
plays rely on any binary relation definable by a finite state transducer. This
solution yields a non-elementary procedure.Comment: (2012
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