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A logical theory for interface specification and verification of distributed, concurrent, interactive, real-time systems is worked out based on a semantic foundation including operational and denotational semantics. It supports a calculus for the specification and verification of concurrent interactive systems by interface assertions. Systems are composed acting concurrently and interacting via streams exchanged over their channels forming feedback loops. A denotational semantics is defined handling feedback communication by recursion and fixpoints based on strong causality and realizability instead of monotonicity. The resulting verification calculus for the specification logic is proved to be sound and relatively complete with respect to an operational semantics in terms of generalized Moore machines. Actually, two models of concurrent systems are defined, a more abstract one with communication and interaction modeled by untimed streams and a more concrete one working with timed streams. The untimed model is an abstraction of the timed model. The timed model allows expressing the laws of causality and realizability. Moreover, the timed model can be used to specify real-time properties. [ABSTRACT FROM AUTHOR]

Abstract: We are interested in separation-logic-based static analysis of programs that use shared mutable data structures. In this paper, we introduce backward and forward analysis for a separation logic called , an extension of separation logic [Ishtiaq and O’Hearn, BI as an assertion language for mutable data structures, in: POPL’01, 2001, pp. 14–26], to which we add fixpoint connectives and postponed substitution. This allows us to express recursive definitions within the logic as well as the axiomatic semantics of while statements. [Copyright &y& Elsevier]