Jan Willem Klop

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Within the context of an algebraic theory of processes, an equational specification of process cooperation is provided. Four cases are considered: free merge or interleaving, merging with communication, merging with mutual exclusion of tight regions, and synchronous process cooperation. The rewrite system behind the communication algebra is shown to be(More)
Contents 1 Abstract Reduction Systems Abstract Term Rewriting Systems play an important role in various areas, such as abstract data type speciications, implementations of functional programming languages and automated deduction. In this chapter we introduce several of the basic concepts and facts for TRS's. Speciically, we discuss Abstract Reduction(More)
Algebraic specifications of abstract data types can often be viewed as systems of rewrite rules. Here we consider rewrite rules with conditions, such as they arise, e.g., from algebraic specifications with positive conditional equations. The conditional term rewriting systems thus obtained which we will study, are based upon the well-known class of(More)
Combinatory Reduction Systems, or CRSs for short, were designed to combine the usual rst-order format of term rewriting with the presence of bound variables as in pure-calculus and various typed-calculi. Bound variables are also present in many other rewrite systems, such as systems with simpliication rules for proof normalization. The original idea of CRSs(More)
A context-free grammar (CFG) in Greibach Normal Form coincides, in another notation, with a system of guarded recursion equations in Basic Process .$dgebrzd. Hence, to each CFG, aprocess can be assigned absolution, which has as its set of finite traces the context-free language (CFL)determined by that CFG. Although theequality problem for CFLs is(More)
We establish some fundamental facts for infinitary orthogonal term rewriting systems (OTRSs): for strongly convergent reductions we prove the Transfinite Parallel Moves Lemma and the Compressing Lemma. Strongness is necessary as shown by counterexamples. Normal forms (which we allow to be infinite) are unique, in contrast to ω-normal forms. Fair reductions(More)