An introduction to assertional reasoning for concurrent systems

Abstract

This is a tutorial introduction to assertional reasoning based on temporal logic. The objective is to provide a working familiarity with the technique. We use a simple system model and a simple proof system, and we keep to a minimum the treatment of issues such as soundness, completeness, compositionality, and abstraction. We model a concurrent system by a state transition system and fairness requirements. We reason about such systems using Hoare logic and a subset of linear-time temporal logic, specifically, invariant assertions and leads-to assertions. We apply the method to several examples.

Symbolic model checking of infinite state systems using presburger arithmetic

“…We use the event-action language from [18] as our syntax for concurrent programs, with a semantics defined in terms of infinite transition systems. A concurrent program C = (V, I, E) is represented by (1) a finite set of data and control variables V; (2) an initial condition I, which specifies the starting states of the program; and (3) a finite set of events E, where each event is considered atomic.…”

Model-checking concurrent systems with unbounded integer variables

“…In this paper we demonstrate our model checker's e ectiveness on some classical in nite-state programs taken from the concurrency literature 3,30]. While relatively small, they possess some interesting subtleties, especially in the tricky way their in nite-state variables in uence control ow.…”

Proof and Evaluation of a 1CS Middleware Data Replication Protocol Based on O2PL

“…In this Section we use a state transition system [9] for describing ERP (introduced in Figure 2). It includes a set of state variables and actions, each one of them subscripted with the node identifier where they are considered.…”

“…For a more detailed description of the correctness proof the reader is referred to [8]. We continue using the notation and definitions of a state transition system [9]. For each ERP's action π, the enabling condition defines a set of state transitions, that is: {(p, π, q), p, q are states; π is an action; p satisfies pre(π); and q is the result of executing eff (π) in p}.…”