Ever since the introduction of behavioral equivalences on processes one has been searching for efficient proof techniques that accompany those equivalences. Both strong bisimilarity and weak bisimilarity are accompanied by an arsenal of up-to techniques: enhancements of their proof methods. For branching bisimilarity, these results have not been established yet. We show that a powerful proof technique is sound for branching bisimilarity by combining the three techniques of up to union, up to expansion and up to context for Bloom's BB cool format. We then make an initial proposal for casting the correctness proof of the up to context technique in an abstract coalgebraic setting, covering branching but also η, delay and weak bisimilarity. ⋆ The research of the second author was supported by a Marie Curie Fellowship (grant code 795119). An extended abstract has been published in the proceedings of SOF-SEM 2020, see https://doi.
Term pattern matching is the problem of finding all pattern matches in a subject term, given a set of patterns. Finding efficient algorithms for this problem is an important direction for research [19]. We present a new set automaton solution for the term pattern matching problem that is based on match set derivatives where each function symbol in the subject pattern is visited exactly once. The algorithm allows for various traversal patterns over the subject term and is particularly suited to search the subject term in parallel.
In previous work we have proposed an efficient pattern matching algorithm based on the notion of set automaton [12]. In this article we investigate how set automata can be exploited to implement efficient term rewriting procedures. These procedures interleave pattern matching steps and rewriting steps and thus smoothly integrate redex discovery and subterm replacement. Concretely, we propose an optimised algorithm for outermost rewriting of left-linear term rewriting systems, prove its correctness, and present the results of some implementation experiments.
Efficient pattern matching is fundamental for practical term rewrite engines.
By preprocessing the given patterns into a finite deterministic automaton the
matching patterns can be decided in a single traversal of the relevant parts of
the input term. Most automaton-based techniques are restricted to linear
patterns, where each variable occurs at most once, and require an additional
post-processing step to check so-called variable consistency. However, we can
show that interleaving the variable consistency and pattern matching phases can
reduce the number of required steps to find all matches. Therefore, we take the
existing adaptive pattern matching automata as introduced by Sekar et al and
extend these with consistency checks. We prove that the resulting deterministic
pattern matching automaton is correct, and show several examples where some
reduction can be achieved.
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