28 research outputs found
How to Handle Assumptions in Synthesis
The increased interest in reactive synthesis over the last decade has led to
many improved solutions but also to many new questions. In this paper, we
discuss the question of how to deal with assumptions on environment behavior.
We present four goals that we think should be met and review several different
possibilities that have been proposed. We argue that each of them falls short
in at least one aspect.Comment: In Proceedings SYNT 2014, arXiv:1407.493
Non-Zero Sum Games for Reactive Synthesis
In this invited contribution, we summarize new solution concepts useful for
the synthesis of reactive systems that we have introduced in several recent
publications. These solution concepts are developed in the context of non-zero
sum games played on graphs. They are part of the contributions obtained in the
inVEST project funded by the European Research Council.Comment: LATA'16 invited pape
Games with Delays. A Frankenstein Approach
We investigate infinite games on finite graphs where the information flow is
perturbed by nondeterministic signalling delays. It is known that such
perturbations make synthesis problems virtually unsolvable, in the general
case. On the classical model where signals are attached to states, tractable
cases are rare and difficult to identify.
Here, we propose a model where signals are detached from control states, and
we identify a subclass on which equilibrium outcomes can be preserved, even if
signals are delivered with a delay that is finitely bounded. To offset the
perturbation, our solution procedure combines responses from a collection of
virtual plays following an equilibrium strategy in the instant- signalling game
to synthesise, in a Frankenstein manner, an equivalent equilibrium strategy for
the delayed-signalling game
Assume-Admissible Synthesis
In this paper, we introduce a novel rule for synthesis of reactive systems,
applicable to systems made of n components which have each their own
objectives. It is based on the notion of admissible strategies. We compare our
novel rule with previous rules defined in the literature, and we show that
contrary to the previous proposals, our rule defines sets of solutions which
are rectangular. This property leads to solutions which are robust and
resilient. We provide algorithms with optimal complexity and also an
abstraction framework.Comment: 31 page
Computer aided synthesis: a game theoretic approach
In this invited contribution, we propose a comprehensive introduction to game
theory applied in computer aided synthesis. In this context, we give some
classical results on two-player zero-sum games and then on multi-player non
zero-sum games. The simple case of one-player games is strongly related to
automata theory on infinite words. All along the article, we focus on general
approaches to solve the studied problems, and we provide several illustrative
examples as well as intuitions on the proofs.Comment: Invitation contribution for conference "Developments in Language
Theory" (DLT 2017
The Complexity of Rational Synthesis
We study the computational complexity of the cooperative and non-cooperative rational synthesis problems, as introduced by Kupferman, Vardi and co-authors. We provide tight results for most of the classical omega-regular objectives, and show how to solve those problems optimally
Assume-Guarantee Synthesis for Concurrent Reactive Programs with Partial Information
Synthesis of program parts is very useful for concurrent systems. However,
most synthesis approaches do not support common design tasks, like modifying a
single process without having to re-synthesize or verify the whole system.
Assume-guarantee synthesis (AGS) provides robustness against modifications of
system parts, but thus far has been limited to the perfect information setting.
This means that local variables cannot be hidden from other processes, which
renders synthesis results cumbersome or even impossible to realize. We resolve
this shortcoming by defining AGS in a partial information setting. We analyze
the complexity and decidability in different settings, showing that the problem
has a high worst-case complexity and is undecidable in many interesting cases.
Based on these observations, we present a pragmatic algorithm based on bounded
synthesis, and demonstrate its practical applicability on several examples
Foundations of Software Science and Computation Structures
We study multi-player turn-based games played on (potentially infinite)
directed graphs. An outcome is assigned to every play of the game. Each player
has a preference relation on the set of outcomes which allows him to compare
plays. We focus on the recently introduced notion of weak subgame perfect
equilibrium (weak SPE). This is a variant of the classical notion of SPE, where
players who deviate can only use strategies deviating from their initial
strategy in a finite number of histories. Having an SPE in a game implies
having a weak SPE but the contrary is generally false.
We propose general conditions on the structure of the game graph and on the
preference relations of the players that guarantee the existence of a weak SPE,
that additionally is finite-memory. From this general result, we derive two
large classes of games for which there always exists a weak SPE: (i) the games
with a finite-range outcome function, and (ii) the games with a finite
underlying graph and a prefix-independent outcome function. For the second
class, we identify conditions on the preference relations that guarantee
memoryless strategies for the weak SPE.Comment: 28 page
Strategy Logic with Imperfect Information
We introduce an extension of Strategy Logic for the imperfect-information
setting, called SLii, and study its model-checking problem. As this logic
naturally captures multi-player games with imperfect information, this problem
is undecidable; but we introduce a syntactical class of "hierarchical
instances" for which, intuitively, as one goes down the syntactic tree of the
formula, strategy quantifications are concerned with finer observations of the
model, and we prove that model-checking SLii restricted to hierarchical
instances is decidable. To establish this result we go through QCTL, an
intermediary, "low-level" logic much more adapted to automata techniques. QCTL
is an extension of CTL with second-order quantification over atomic
propositions. We extend it to the imperfect information setting by
parameterising second-order quantifiers with observations. While the
model-checking problem of QCTLii is, in general, undecidable, we identify a
syntactic fragment of hierarchical formulas and prove, using an
automata-theoretic approach, that it is decidable. We apply our result to solve
complex strategic problems in the imperfect-information setting. We first show
that the existence of Nash equilibria for deterministic strategies is decidable
in games with hierarchical information. We also introduce distributed rational
synthesis, a generalisation of rational synthesis to the imperfect-information
setting. Because it can easily be expressed in our logic, our main result
provides solution to this problem in the case of hierarchical information.Comment: arXiv admin note: text overlap with arXiv:1805.1259