Parameterized Synthesis

Jacobs, Swen; Bloem, Roderick

doi:10.1007/978-3-642-28756-5_25

Cited by 23 publications

(20 citation statements)

References 31 publications

(23 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, it is also perfectly natural to consider uniform local strategies where each process only sees its own actions and possibly those that are revealed according to some causal dependencies. This is, e.g., the setting considered in [3,18] for a fixed number of processes and in [25] for parameterized systems over ring architectures.…”

Section: Resultsmentioning

confidence: 99%

Parameterized Synthesis for Fragments of First-Order Logic Over Data Words

Bérard¹,

Bollig²,

Lehaut³

et al. 2020

Lecture Notes in Computer Science

View full text Add to dashboard Cite

We study the synthesis problem for systems with a parameterized number of processes. As in the classical case due to Church, the system selects actions depending on the program run so far, with the aim of fulfilling a given specification. The difficulty is that, at the same time, the environment executes actions that the system cannot control. In contrast to the case of fixed, finite alphabets, here we consider the case of parameterized alphabets. An alphabet reflects the number of processes, which is static but unknown. The synthesis problem then asks whether there is a finite number of processes for which the system can satisfy the specification. This variant is already undecidable for very limited logics. Therefore, we consider a first-order logic without the order on word positions. We show that even in this restricted case synthesis is undecidable if both the system and the environment have access to all processes. On the other hand, we prove that the problem is decidable if the environment only has access to a bounded number of processes. In that case, there is even a cutoff meaning that it is enough to examine a bounded number of process architectures to solve the synthesis problem. Partly supported by ANR FREDDA (ANR-17-CE40-0013).

show abstract

Section: Resultsmentioning

confidence: 99%

Parameterized Synthesis for Fragments of First-Order Logic Over Data Words

Bérard¹,

Bollig²,

Lehaut³

et al. 2020

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…We believe that our results will fertilize synthesis of parameterized systems [18] and more classical questions whose theoretical foundations go back to the 50s and Church's synthesis problem. Let us cite Brütsch and Thomas, who observed a lack of approaches to synthesis over infinite alphabets [11]: "It is remarkable, however, that a different kind of 'infinite extension' of the Büchi-Landweber Theorem has not been addressed in the literature, namely the case where the input alphabet over which ω-sequences are formed is infinite."…”

Section: Introductionmentioning

confidence: 86%

Round-Bounded Control of Parameterized Systems

Bollig

Lehaut

Sznajder

2018

Automated Technology for Verification and Analysis

View full text Add to dashboard Cite

We consider systems with unboundedly many processes that communicate through shared memory. In that context, simple verification questions have a high complexity or, in the case of pushdown processes, are even undecidable. Good algorithmic properties are recovered under round-bounded verification, which restricts the system behavior to a bounded number of round-robin schedules. In this paper, we extend this approach to a game-based setting. This allows one to solve synthesis and control problems and constitutes a further step towards a theory of languages over infinite alphabets.

show abstract

“…Therefore it is sufficient to design an algorithm for the special case of f = 1 and n = 4. From the perspective of parametrised verification and synthesis, the following lemma can be regarded as a cut-off result [26,36].…”

Section: Increasing the Number Of Nodesmentioning

confidence: 99%

Synchronous counting and computational algorithm design

Dolev

Heljanko

Järvisalo

et al. 2016

Journal of Computer and System Sciences

View full text Add to dashboard Cite

Abstract. Consider a complete communication network on n nodes, each of which is a state machine. In synchronous 2-counting, the nodes receive a common clock pulse and they have to agree on which pulses are "odd" and which are "even". We require that the solution is self-stabilising (reaching the correct operation from any initial state) and it tolerates f Byzantine failures (nodes that send arbitrary misinformation). Prior algorithms are expensive to implement in hardware: they require a source of random bits or a large number of states.This work consists of two parts. In the first part, we use computational techniques (often known as synthesis) to construct very compact deterministic algorithms for the first non-trivial case of f = 1. While no algorithm exists for n < 4, we show that as few as 3 states per node are sufficient for all values n ≥ 4. Moreover, the problem cannot be solved with only 2 states per node for n = 4, but there is a 2-state solution for all values n ≥ 6.In the second part, we develop and compare two different approaches for synthesising synchronous counting algorithms. Both approaches are based on casting the synthesis problem as a propositional satisfiability (SAT) problem and employing modern SATsolvers. The difference lies in how to solve the SAT problem: either in a direct fashion, or incrementally within a counter-example guided abstraction refinement loop. Empirical results suggest that the former technique is more efficient if we want to synthesise time-optimal algorithms, while the latter technique discovers non-optimal algorithms more quickly.

show abstract

Parameterized Synthesis

Cited by 23 publications

References 31 publications

Parameterized Synthesis for Fragments of First-Order Logic Over Data Words

Parameterized Synthesis for Fragments of First-Order Logic Over Data Words

Round-Bounded Control of Parameterized Systems

Synchronous counting and computational algorithm design

Contact Info

Product

Resources

About