108 research outputs found
The Determinacy of Context-Free Games
We prove that the determinacy of Gale-Stewart games whose winning sets are
accepted by real-time 1-counter B\"uchi automata is equivalent to the
determinacy of (effective) analytic Gale-Stewart games which is known to be a
large cardinal assumption. We show also that the determinacy of Wadge games
between two players in charge of omega-languages accepted by 1-counter B\"uchi
automata is equivalent to the (effective) analytic Wadge determinacy. Using
some results of set theory we prove that one can effectively construct a
1-counter B\"uchi automaton A and a B\"uchi automaton B such that: (1) There
exists a model of ZFC in which Player 2 has a winning strategy in the Wadge
game W(L(A), L(B)); (2) There exists a model of ZFC in which the Wadge game
W(L(A), L(B)) is not determined. Moreover these are the only two possibilities,
i.e. there are no models of ZFC in which Player 1 has a winning strategy in the
Wadge game W(L(A), L(B)).Comment: To appear in the Proceedings of the 29 th International Symposium on
Theoretical Aspects of Computer Science, STACS 201
Customizing BPMN Diagrams Using Timelines
BPMN (Business Process Model and Notation) is widely used standard modeling technique for representing Business Processes by using diagrams, but lacks in some aspects. Representing execution-dependent and time-dependent decisions in BPMN Diagrams may be a daunting challenge [Carlo Combi et al., 2017]. In many cases such constraints are omitted in order to preserve the simplicity and the readability of the process model. However, for purposes such as compliance checking, process mining, and verification, formalizing such constraints could be very useful. In this paper, we propose a novel approach for annotating BPMN Diagrams with Temporal Synchronization Rules borrowed from the timeline-based planning field. We discuss the expressivity of the proposed approach and show that it is able to capture a lot of complex temporally-related constraints without affecting the structure of BPMN diagrams. Finally, we provide a mapping from annotated BPMN diagrams to timeline-based planning problems that allows one to take advantage of the last twenty years of theoretical and practical developments in the field
Observation and Distinction. Representing Information in Infinite Games
We compare two approaches for modelling imperfect information in infinite games by using finite-state automata. The first, more standard approach views information as the result of an observation process driven by a sequential Mealy machine. In contrast, the second approach features indistinguishability relations described by synchronous two-tape automata.
The indistinguishability-relation model turns out to be strictly more expressive than the one based on observations. We present a characterisation of the indistinguishability relations that admit a representation as a finite-state observation function. We show that the characterisation is decidable, and give a procedure to construct a corresponding Mealy machine whenever one exists
AbsSynthe: abstract synthesis from succinct safety specifications
In this paper, we describe a synthesis algorithm for safety specifications
described as circuits. Our algorithm is based on fixpoint computations,
abstraction and refinement, it uses binary decision diagrams as symbolic data
structure. We evaluate our tool on the benchmarks provided by the organizers of
the synthesis competition organized within the SYNT'14 workshop.Comment: In Proceedings SYNT 2014, arXiv:1407.493
Multiplayer Cost Games with Simple Nash Equilibria
Multiplayer games with selfish agents naturally occur in the design of
distributed and embedded systems. As the goals of selfish agents are usually
neither equivalent nor antagonistic to each other, such games are non zero-sum
games. We study such games and show that a large class of these games,
including games where the individual objectives are mean- or discounted-payoff,
or quantitative reachability, and show that they do not only have a solution,
but a simple solution. We establish the existence of Nash equilibria that are
composed of k memoryless strategies for each agent in a setting with k agents,
one main and k-1 minor strategies. The main strategy describes what happens
when all agents comply, whereas the minor strategies ensure that all other
agents immediately start to co-operate against the agent who first deviates
from the plan. This simplicity is important, as rational agents are an
idealisation. Realistically, agents have to decide on their moves with very
limited resources, and complicated strategies that require exponential--or even
non-elementary--implementations cannot realistically be implemented. The
existence of simple strategies that we prove in this paper therefore holds a
promise of implementability.Comment: 23 page
Decision Problems for Nash Equilibria in Stochastic Games
We analyse the computational complexity of finding Nash equilibria in
stochastic multiplayer games with -regular objectives. While the
existence of an equilibrium whose payoff falls into a certain interval may be
undecidable, we single out several decidable restrictions of the problem.
First, restricting the search space to stationary, or pure stationary,
equilibria results in problems that are typically contained in PSPACE and NP,
respectively. Second, we show that the existence of an equilibrium with a
binary payoff (i.e. an equilibrium where each player either wins or loses with
probability 1) is decidable. We also establish that the existence of a Nash
equilibrium with a certain binary payoff entails the existence of an
equilibrium with the same payoff in pure, finite-state strategies.Comment: 22 pages, revised versio
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