3,951 research outputs found
Translating Asynchronous Games for Distributed Synthesis (Full Version)
In distributed synthesis, we generate a set of process implementations that,
together, accomplish an objective against all possible behaviors of the
environment. A lot of recent work has focussed on systems with causal memory,
i.e., sets of asynchronous processes that exchange their causal histories upon
synchronization. Decidability results for this problem have been stated either
in terms of control games, which extend Zielonka's asynchronous automata by
partitioning the actions into controllable and uncontrollable, or in terms of
Petri games, which extend Petri nets by partitioning the tokens into system and
environment players. The precise connection between these two models was so
far, however, an open question. In this paper, we provide the first formal
connection between control games and Petri games. We establish the equivalence
of the two game models based on weak bisimulations between their strategies.
For both directions, we show that a game of one type can be translated into an
equivalent game of the other type. We provide exponential upper and lower
bounds for the translations. Our translations make it possible to transfer and
combine decidability results between the two types of games. Exemplarily, we
translate decidability in acyclic communication architectures, originally
obtained for control games, to Petri games, and decidability in single-process
systems, originally obtained for Petri games, to control games
Translating Asynchronous Games for Distributed Synthesis
In distributed synthesis, a set of process implementations is generated, which together, accomplish an objective against all possible behaviors of the environment. A lot of recent work has focussed on systems with causal memory, i.e., sets of asynchronous processes that exchange their causal histories upon synchronization. Decidability results for this problem have been stated either in terms of control games, which extend Zielonka's asynchronous automata by partitioning the actions into controllable and uncontrollable, or in terms of Petri games, which extend Petri nets by partitioning the tokens into system and environment players. The precise connection between these two models was so far, however, an open question.
In this paper, we provide the first formal connection between control games and Petri games. We establish the equivalence of the two game types based on weak bisimulations between their strategies. For both directions, we show that a game of one type can be translated into an equivalent game of the other type. We provide exponential upper and lower bounds for the translations. Our translations allow to transfer and combine decidability results between the two types of games. Exemplarily, we translate decidability in acyclic communication architectures, originally obtained for control games, to Petri games, and decidability in single-process systems, originally obtained for Petri games, to control games
A guided tour of asynchronous cellular automata
Research on asynchronous cellular automata has received a great amount of
attention these last years and has turned to a thriving field. We survey the
recent research that has been carried out on this topic and present a wide
state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat
Global Winning Conditions in Synthesis of Distributed Systems with Causal Memory
In the synthesis of distributed systems, we automate the development of distributed programs and hardware by automatically deriving correct implementations from formal specifications. For synchronous distributed systems, the synthesis problem is well known to be undecidable. For asynchronous systems, the boundary between decidable and undecidable synthesis problems is a long-standing open question. We study the problem in the setting of Petri games, a framework for distributed systems where asynchronous processes are equipped with causal memory. Petri games extend Petri nets with a distinction between system places and environment places. The components of a distributed system are the players of the game, represented as tokens that exchange information during each synchronization. Previous decidability results for this model are limited to local winning conditions, i.e., conditions that only refer to individual components.
In this paper, we consider global winning conditions such as mutual exclusion, i.e., conditions that refer to the state of all components. We provide decidability and undecidability results for global winning conditions. First, we prove for winning conditions given as bad markings that it is decidable whether a winning strategy for the system players exists in Petri games with a bounded number of system players and one environment player. Second, we prove for winning conditions that refer to both good and bad markings that it is undecidable whether a winning strategy for the system players exists in Petri games with at least two system players and one environment player. Our results thus show that, on the one hand, it is indeed possible to use global safety specifications like mutual exclusion in the synthesis of distributed systems. However, on the other hand, adding global liveness specifications results in an undecidable synthesis problem for almost all Petri games
Synthesis from multi-paradigm specifications
This work proposes a language for describing reactive synthesis problems that integrates imperative and declarative elements. The semantics is defined in terms of two-player turn-based infinite games with full information. Currently, synthesis tools accept linear temporal logic (LTL) as input, but this description is less structured and does not facilitate the expression of sequential constraints. This motivates the use of a structured programming language to specify synthesis problems. Transition systems and guarded commands serve as imperative constructs, expressed in a syntax based on that of the modeling language Promela. The syntax allows defining which player controls data and control flow, and separating a program into assumptions and guarantees. These notions are necessary for input to game solvers. The integration of imperative and declarative paradigms allows using the paradigm that is most appropriate for expressing each requirement. The declarative part is expressed in the LTL fragment of generalized reactivity(1), which admits efficient synthesis algorithms. The implementation translates Promela to input for the Slugs synthesizer and is written in Python
Symmetric Synthesis
We study the problem of determining whether a given temporal specification can be implemented by a symmetric system, i.e., a system composed from identical components. Symmetry is an important goal in the design of distributed systems, because systems that are composed from identical components are easier to build and maintain. We show that for the class of rotation-symmetric architectures, i.e., multi-process architectures where all processes have access to all system inputs, but see different rotations of the inputs, the symmetric synthesis problem is EXPTIME-complete in the number of processes. In architectures where the processes do not have access to all input variables, the symmetric synthesis problem becomes undecidable, even in cases where the standard distributed synthesis problem is decidable
On verifying timed hyperproperties
We study the satisfiability and model-checking problems for timed
hyperproperties specified with HyperMTL, a timed extension of HyperLTL.
Depending on whether interleaving of events in different traces is allowed, two
possible semantics can be defined for timed hyperproperties: asynchronous and
synchronous. While the satisfiability problem can be decided similarly to
HyperLTL regardless of the choice of semantics, we show that the model-checking
problem, unless the specification is alternation-free, is undecidable even when
very restricted timing constraints are allowed. On the positive side, we show
that model checking HyperMTL with quantifier alternations is possible under
certain conditions in the synchronous semantics, or when there is a fixed bound
on the length of the time domain.EP/K026399/1 and EP/P020011/
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