Automated Verification, Synthesis and Correction of Concurrent Systems via MSO Logic (1402.2698v1)

Abstract: In this work we provide algorithmic solutions to five fundamental problems concerning the verification, synthesis and correction of concurrent systems that can be modeled by bounded p/t-nets. We express concurrency via partial orders and assume that behavioral specifications are given via monadic second order logic. A c-partial-order is a partial order whose Hasse diagram can be covered by c paths. For a finite set T of transitions, we let P(c,T,\phi) denote the set of all T-labelled c-partial-orders satisfying \phi. If N=(P,T) is a p/t-net we let P(N,c) denote the set of all c-partially-ordered runs of N. A (b, r)-bounded p/t-net is a b-bounded p/t-net in which each place appears repeated at most r times. We solve the following problems: 1. Verification: given an MSO formula \phi and a bounded p/t-net N determine whether P(N,c)\subseteq P(c,T,\phi), whether P(c,T,\phi)\subseteq P(N,c), or whether P(N,c)\cap P(c,T,\phi)=\emptyset. 2. Synthesis from MSO Specifications: given an MSO formula \phi, synthesize a semantically minimal (b,r)-bounded p/t-net N satisfying P(c,T,\phi)\subseteq P(N, c). 3. Semantically Safest Subsystem: given an MSO formula \phi defining a set of safe partial orders, and a b-bounded p/t-net N, possibly containing unsafe behaviors, synthesize the safest (b,r)-bounded p/t-net N' whose behavior lies in between P(N,c)\cap P(c,T,\phi) and P(N,c). 4. Behavioral Repair: given two MSO formulas \phi and \psi, and a b-bounded p/t-net N, synthesize a semantically minimal (b,r)-bounded p/t net N' whose behavior lies in between P(N,c) \cap P(c,T,\phi) and P(c,T,\psi). 5. Synthesis from Contracts: given an MSO formula \phi^yes specifying a set of good behaviors and an MSO formula \phi^no specifying a set of bad behaviors, synthesize a semantically minimal (b,r)-bounded p/t-net N such that P(c,T,\phi^yes) \subseteq P(N,c) but P(c,T,\phi^no ) \cap P(N,c)=\emptyset.