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One day, you will discover a new adventure and knowledge by spending more money. But when? Do you think that you need to obtain those all requirements when having much money? Why don't you try to get something simple at first? That's something that will lead you to know more about the world, adventure, some places, history, entertainment, and more? It is(More)
A temporal language and system are presented which are based on branching time structure. By the introduction of symmetrically dual sets of temporal operators, it is possible to discuss properties which hold either along one path or along all paths. Consequently it is possible to express in this system all the properties that were previously expressible in(More)
Motivated by applications to program verification, we study a decision procedure for satisfiability in an expressive fragment of a theory of arrays, which is parameterized by the theories of the array elements. The decision procedure reduces satisfiability of a formula of the fragment to satisfiability of an equisatisfiable quantifier-free formula in the(More)
In this work we show that it is possible to formalize all properties regularly observed in (deterministic and non-deterministic) algorithms in second-order predicate calculus. Moreover, we show that for any given algorithm it suffices to know how to formalize its 'partial correctness' by a second-order formula in order to formalize all other properties by(More)
A common tool for proving the termination of programs is the <italic>well-founded set</italic>, a set ordered in such a way as to admit no infinite descending sequences. The basic approach is to find a <italic>termination function</italic> that maps the values of the program variables into some well-founded set, such that the value of the termination(More)
In this paper, Propositional Temporal Logic (PTL) is applied to the specification and synthesis of the synchronization part of communicating processes. To specify a process, a PTL formula that describes its sequence of communications is given. The synthesis is done by constructing a model of the given specifications using a tableau-like satisfiability(More)
We propose a classification of temporal properties int!o a, hierarchy which refines the known safety-Ziveness classifica,tion of properties. The new classification secognizes the cla.sses of safety, guarantee, persistence, fairness, and hyper-fairn,ess. The cla,ssifica,tion suggested here is based on the diRerent< wa,ys a, property of fin&e computa,tions(More)
We present a new technique for the generation of non-linear (algebraic) invariants of a program. Our technique uses the theory of ideals over polynomial rings to reduce the non-linear invariant generation problem to a numerical constraint solving problem. So far, the literature on invariant generation has been focussed on the construction of linear(More)