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

Tree pattern matching from regular tree expressions

summary:In this work we deal with tree pattern matching over ranked trees, where the pattern set to be matched against is defined by a regular tree expression. We present a new method that uses a tree automaton constructed inductively from a regular tree expression. First we construct a special tree automaton for the regular tree expression of the pattern $E$, which is somehow a generalization of Thompson automaton for strings. Then we run the constructed automaton on the subject tree $t$. The pattern matching algorithm requires an $\mathcal{O}(\vert t\vert\vert E\vert)$ time complexity, where $\vert t\vert$ is the number of nodes of $t$ and $\vert E\vert$ is the size of the regular tree expression $E$. The novelty of this contribution besides the low time complexity is that the set of patterns can be infinite, since we use regular tree expressions to represent patterns

A minimal integer automaton behind crystal plasticity

Power law fluctuations and scale free spatial patterns are known to characterize steady state plastic flow in crystalline materials. In this Letter we study the emergence of correlations in a simple Frenkel-Kontorova (FK) type model of 2D plasticity which is largely free of arbitrariness, amenable to analytical study and is capable of generating critical exponents matching experiments. Our main observation concerns the possibility to reduce continuum plasticity to an integer valued automaton revealing inherent discreteness of the plastic flow.Comment: 4 pages, 5 figure

LNCS

We provide a procedure for detecting the sub-segments of an incrementally observed Boolean signal ω that match a given temporal pattern ϕ. As a pattern specification language, we use timed regular expressions, a formalism well-suited for expressing properties of concurrent asynchronous behaviors embedded in metric time. We construct a timed automaton accepting the timed language denoted by ϕ and modify it slightly for the purpose of matching. We then apply zone-based reachability computation to this automaton while it reads ω, and retrieve all the matching segments from the results. Since the procedure is automaton based, it can be applied to patterns specified by other formalisms such as timed temporal logics reducible to timed automata or directly encoded as timed automata. The procedure has been implemented and its performance on synthetic examples is demonstrated

Target Code Selection by Tilling AST with the Use of Tree Pattern Pushdown Automaton

A new and simple method for target code selection by tilling an abstract syntax tree is presented. As it is usual, tree patterns corresponding to target machine instructions are matched in the abstract syntax tree. Matching tree patterns is performed with the use of tree pattern pushdown automaton, which accepts all tree patterns matching the abstract syntax tree in the linear postfix bar notation and represents a full index of the abstract syntax tree for tree patterns. The use of the index allows to match patterns quickly, in time depending on the size of patterns and not depending on the size of the tree. The selection of a particular target instruction corresponds to a modification of the abstract syntax tree and also a corresponding incremental modification of the index is performed. A reference to a fully functional prototype is provided