We present a logic for relating heap-manipulating programs to numeric abstractions. These numeric abstractions are expressed as simple imperative programs over integer variables and have the property that termination and safety of the numeric program ensures termination and safety of the original, heap-manipulating program. We have implemented an automated version of this abstraction process and present experimental results for programs involving a variety of data structures.

Abstract We introduce a graphical interactive tool, named GOAL, that can assist the user in understanding Büchi automata, linear temporal logic, and their relation. Büchi automata and linear temporal logic are closely related and have long served as fundamental building blocks of linear-time model checking. Understanding their relation is instrumental in discovering algorithmic solutions to model checking problems or simply in using those solutions, e.g., specifying a temporal property directly by an automaton rather than a temporal formula so that the property can be verified by an algorithm that operates on automata. One main function of the GOAL tool is translation of a temporal formula into an equivalent Büchi automaton that can be further manipulated visually. The user may edit the resulting automaton, attempting to optimize it, or simply run the automaton on some inputs to get a basic understanding of how it operates. GOAL includes a large number of translation algorithms, most of which support past temporal operators. With the option of viewing the intermediate steps of a translation, the user can quickly grasp how a translation algorithm works. The tool also provides various standard operations and tests on Büchi automata, in particular the equivalence test which is essential for checking if a hand-drawn automaton is correct in the sense that it is equivalent to some intended temporal formula or reference automaton. Several use cases are elaborated to show how these GOAL functions may be combined to facilitate the learning and teaching of Büchi automata and linear temporal logic.

Over the last few years there has been an increasing research effort directed towards the automatic verification of infinite state systems. This paper is concerned with identifying general mathematical structures which can serve as sufficient conditions for achieving decidability. We present decidability results for a class of systems (called well-structured systems), which consist of a finite control part operating on an infinite data domain. The results assume that the data domain is equipped with a well-ordered and well-founded preorder such that the transition relation is "monotonic" (is a simulation) with respect to the preorder. We show that the following properties are decidable for well-structured systems: reachability; eventuality; and simulation. We also describe how these general principles subsume several decidability results from the literature about timed automata, relational automata, Petri nets, and lossy channel systems.

We explore the use of UNITY logic in specifying and verifying fairness properties of UNITY and UNITY-like programs whose semantics can be modeled by weakly fair transition systems. For such programs, strong fairness properties in the form of “if p holds infinitely often then q also holds infinitely often □◊p⇒□◊q, can be expressed as conditional UNITY properties of the form of “Hypothesis: true→p Conclusion:true→q”. We show that UNITY logic is relatively complete for proving such properties; in the process, a simple inference rule is derived. Specification and verification of weak fairness properties are also discussed.

The implementation of nondeterministic pairwise synchronous communication among a set of asynchronous processes is modeled as the binary interaction problem. The paper describes an algorithm for this problem that satisfies a strong fairness property that guarantees freedom from process starvation. This is the first algorithm for binary interactions with strong fairness whose message cost and response time are independent of the total number of processes in the system. The paper also describes how the fair algorithm may be extended to tolerate detectable fail-stop failures. Finally, we show how any solution to the dining philosophers problem can be embedded to design a fair algorithm for binary interactions. In particular, this embedding is used to derive a fair algorithm that can cope with undetectable fail-stop failures.>

The implementation of nondeterministic pairwise synchronous communication among a set of asynchronous processes is modeled as a binary interaction problem. An algorithm for this problem, which satisfies a strong fairness property that guarantees freedom from process starvation, is described. The message and time complexities are independent of the total number of processes in the system. The ways in which the algorithm may be extended to cope with fail-stop process failures are discussed.>