## Reasoning about Systems with Many Processes (1992)

Venue: | Journal of the ACM |

Citations: | 128 - 2 self |

### BibTeX

@ARTICLE{German92reasoningabout,

author = {Stevenm German and A. Prasad Sistla},

title = {Reasoning about Systems with Many Processes},

journal = {Journal of the ACM},

year = {1992},

volume = {39},

pages = {675--735}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. Methods are given for automatically verifying temporal properties of concurrent systems containing an arbitrary number of finite-state processes that communicate using CCS actions. Two models of systems are considered. Systems in the first model consist of a unique contro [ process and an arbitrary number of user processes with identical det-lnitions, For this model, a decision procedure to check whether all the executions of a process satisfy a given specification is presented. This algorithm runs in time double exponential mthe sizes of the control andthe user process definitions. It is also proven that it is decidable whether all the fair executions of a process satisfy a gwen specification. The second model is a special case of the first. In this model, all the processes have identical definitions. For this model, an efficient decision procedure is presented that checks if every execution of a process satisfies a given temporal logic specification. This algorithm runs in time polynomial inthesize of the process definition. Itisshown howtoverify certamglobal properties such as mutual exchrslon and absence of deadlocks. Finally, it is shown how these decision procedures can beusedto reason about certain systems with a communication network,

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Citation Context ...cessary It can be shown that the modelcheckmg problem under fan’ness can be reduced to the reachability problem for a VASS of dimension only 4 m + 5, where m is the number of states of a user process =-=[31]-=- THEOREM 3.15. The model-checking problem for fair computations of the user process is decidable. PROOF. We prove the theorem by reducing this problem to the modelchecking problem for fair computation... |

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Citation Context ...t is, we have to construct an automaton that accepts the set of strings that are not accepted by B. We modify the present algorithms by using B’ in place of the autpmaton A .f. Using the algorithm of =-=[32]-=-, we can obtain B’ in time 0(16 I~1-), and such that I B’ I s 16 l~l-. In this case, the algorithm given in Section 3 for the first model of processes without fairness will have time complexity double... |

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Citation Context ...s of automata are given using a fixed encoding, and we let size(A) denote the length of this encoding for A. The connection between automata and temporal logic has been investigated in [6], [28], and =-=[34]-=-. Throughout the paper, we make use of the following fact that has been established in these papers: Corresponding to every PTL formula f, there is an automaton A ~ with input alphabet 2 ~’that accept... |