Optimal Zielonka-Type Construction of Deterministic Asynchronous Automata

Genest, Blaise; Gimbert, Hugo; Muscholl, Anca; Walukiewicz, Igor

doi:10.1007/978-3-642-14162-1_5

Cited by 15 publications

(11 citation statements)

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“…Many researchers contributed to simplify the construction and to improve its complexity, see [8,33,19,16] and references therein. The most recent construction [16] produces deterministic Zielonka automata of size that is exponential in the number of processes (and polynomial in the size of a DFA for L). The exponential dependence on the number of processes is necessary, modulo a technical assumption (that is actually required for monitoring).…”

Section: Mazurkiewicz Traces and Zielonka's Theoremmentioning

confidence: 99%

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Automated Synthesis of Distributed Controllers

Muscholl

2015

Automata, Languages, and Programming

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Abstract. Synthesis is a particularly challenging problem for concurrent programs. At the same time it is a very promising approach, since concurrent programs are difficult to get right, or to analyze with traditional verification techniques. This paper gives an introduction to distributed synthesis in the setting of Mazurkiewicz traces, and its applications to decentralized runtime monitoring. ContextModern computing systems are increasingly distributed and heterogeneous. Software needs to be able to exploit these advances, providing means for applications to be more performant. Traditional concurrent programming paradigms, as in Java, are based on threads, shared-memory, and locking mechanisms that guard access to common data. More recent paradigms like the reactive programming model of Erlang [4] and Scala [35,36] replace shared memory by asynchronous message passing, where sending a message is non-blocking.In all these concurrent frameworks, writing reliable software is a serious challenge. Programmers tend to think about code mostly in a sequential way, and it is hard to grasp all possible schedulings of events in a concurrent execution. For similar reasons, verification and analysis of concurrent programs is a difficult task. Testing, which is still the main method for error detection in software, has low coverage for concurrent programs. The reason is that bugs in such programs are difficult to reproduce: they may happen under very specific thread schedules and the likelihood of taking such corner-case schedules is very low. Automated verification, such as model-checking and other traditional exploration techniques, can handle very limited instances of concurrent programs, mostly because of the very large number of possible states and of possible interleavings of executions.Formal analysis of programs requires as a pre-requisite a clean mathematical model for programs. Verification of sequential programs starts usually with an abstraction step -reducing the value domains of variables to finite domains, viewing conditional branching as non-determinism, etc. Another major simplification consists in disallowing recursion. This leads to a very robust computational model, namely finite-state automata and regular languages. Regular languages of words (and trees) are particularly well understood notions. The deep connections between logic and automata revealed by the foundational work of Büchi, Rabin, and others, are the main ingredients in automata-based verification.

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Section: Mazurkiewicz Traces and Zielonka's Theoremmentioning

confidence: 99%

“…This can be achieved by asking that in every global state of A M such that no process is in a rejecting state, every action is enabled. A related discussion on desirable properties of Zielonka automata and on implementating the construction of [16] is reported in [2].…”

Section: Theorem 3 ([23]mentioning

confidence: 99%

Automated Synthesis of Distributed Controllers

Muscholl

2015

Automata, Languages, and Programming

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“…[22] Let dom : Σ → (2 P \ {∅}) be a distribution of letters. If a language L ⊆ Σ * is regular and trace-closed then there is a deterministic Zielonka automaton accepting L (of size exponential in the number of processes and polynomial in the size of the minimal automaton for L, see [8]).…”

Section: Zielonka Automatamentioning

confidence: 99%

Asynchronous Games over Tree Architectures

Genest

Gimbert

Muscholl

et al. 2013

Automata, Languages, and Programming

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Abstract. We consider the distributed control problem in the setting of Zielonka asynchronous automata. Such automata are compositions of finite processes communicating via shared actions and evolving asynchronously. Most importantly, processes participating in a shared action can exchange complete information about their causal past. This gives more power to controllers, and avoids simple pathological undecidable cases as in the setting of Pnueli and Rosner. We show the decidability of the control problem for Zielonka automata over acyclic communication architectures. We provide also a matching lower bound, which is l-fold exponential, l being the height of the architecture tree.

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“…[10,30,19,17]). Currently the best construction starting with a DFA A is polynomial in the size of A and simply exponential in the number of processes.…”

Section: Example 1 Let Us Consider the Asynchronous Automatonmentioning

confidence: 99%

“…Currently the best construction starting with a DFA A is polynomial in the size of A and simply exponential in the number of processes. Surprisingly, it is rather difficult to come up with a matching lower bound (see [17] for partial results). As explained in Section 3, this construction plays a fundamental role in other settings of distributed synthesis, as for instance for communicating automata, that we present next.…”

Section: Example 1 Let Us Consider the Asynchronous Automatonmentioning

confidence: 99%