Synthesis of concurrent systems with many similar processes

Abstract

Methods for synthesizing concurrent programs from temporal logic specifications based on the use of a decision procedure for testing temporal satisfiability have been proposed by Emerson and Clarke and by Manna and Wolper. An important advantage of these synthesis methods is that they obviate the need to manually compose a program and manually construct a proof of its correctness. One only has to formulate a precise problem specification; the synthesis method then mechanically constructs a correct solution. A serious drawback of these methods in practice, however, is that they suffer from the state explosion problem. To synthesize a concurrent system consisting of K sequential processes, each having N states in its local transition diagram, requires construction of the global product-machine having about N K global states in general. This exponential growth in K makes it infeasible to synthesize systems composed of more than 2 or 3 processes. In this article, we show how to synthesize concurrent systems consisting of many (i.e., a finite but arbitrarily large number K of) similar sequential processes. Our approach avoids construction of the global product-machine for K processes; instead, it constructs a two-process product-machine for a single pair of generic sequential processes. The method is uniform in K, providing a simple template that can be instantiated for each process to yield a solution for any fixed K. The method is also illustrated on synchronization problems from the literature.A preliminary version of some of these results was presented at the ACM Symposium on Principles

Reducing Model Checking of the Many to the Few

“…But these results were formulated only for a single process class and, for a restricted version of the token ring model, namely one where the token cannot be used to pass values. Also, related are the results of Attie and Emerson [AE98]. In the context of program synthesis, rather than program verification, it is shown how certain l -process solutions to synchronization problems could be inflated to 0 -process solutions.…”

Mechanical Verification of Automatic Synthesis of Fault-Tolerant Programs

“…In [16], Emerson and Clarke propose an algorithm that synthesizes a program from its temporal logic specification. Since then, other algorithms have been proposed in the literature [17][18][19]. In the previous work prior to [7], the input to synthesis algorithms is either an automaton or temporal logics specification and any modification in the specification requires synthesizing the new program from scratch.…”

Model and program repair via SAT solving

“…We can both fix the protocol and require the result to be symmetric in P 1 and P 2 (i.e., the code for P 2 results from interchanging the process indices 1 and 2 in the code for P 1 [3]) by adding the conjunct N s ≡ N t for every pair of symmetric state s, t, i.e., such that t results from s by interchanging the process indices 1 and 2, and likewise for symmetric transitions (start and end states are symmetric).…”