7 research outputs found
Adaptive Non-Linear Pattern Matching Automata
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 a match all matches. Therefore, we take the existing adaptive pattern matching automata as introduced by Sekar et al and extend it these with consistency checks. We prove that the resulting deterministic pattern matching automaton is correct, and show that its evaluation depth is can be shorter than two-phase approaches
Up-to Techniques for Branching Bisimilarity
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 {\eta}, delay and weak
bisimilarity
Adaptive Non-linear Pattern Matching Automata
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
Term Rewriting Based On Set Automaton Matching
In previous work we have proposed an efficient pattern matching algorithm
based on the notion of set automaton. 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.Comment: Technical report to accompany a submission to FSCD 202
Adaptive Non-Linear Pattern Matching Automata
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 a match all matches. Therefore, we take the existing adaptive pattern matching automata as introduced by Sekar et al and extend it these with consistency checks. We prove that the resulting deterministic pattern matching automaton is correct, and show that its evaluation depth is can be shorter than two-phase approaches
Up-to techniques for branching bisimilarity
\u3cp\u3eEver 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, delay and weak bisimilarity.\u3c/p\u3
Up-to techniques for branching bisimilarity
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, delay and weak bisimilarity