Adaptive Pattern Matching

Abstract

Pattern matching is an important operation used in many applications such as functional programming, rewriting and rule-based expert systems. By preprocessing the patterns into a DFA-like automaton, we can rapidly select the matching pattern(s) in a single scan of the relevant portions of the input term. This automaton is typically based on left-to-right traversal (of the patterns) or its variants. By adapting the traversal order to suit the set of input patterns, it is possible to considerably reduce the space and matching time requirements of the automaton. The design of such adaptive automata is the focus of this paper. In this context we study several important problems that have remained open even for automata based on left-to-right traversals. Such problems include upper and lower bounds on space complexity, construction of optimal dag automata and impact of typing in pattern matching. An interesting consequence of our results is that lazy pattern matching in typed systems (such as ML) is computationally hard whereas it can be done e ciently in untyped systems.

A generic algorithm for checking exhaustivity of pattern matching (short paper)

“…The general problem of pattern matching is NP-Complete [10]. Thus we expect the worst-case performance of the generic algorithm to be exponential.…”

GADTs meet their match: pattern-matching warnings that account for GADTs, guards, and laziness

“…The size of the uncovered set is the square of the number of constructors in T. It gets worse: Sekar et al [26] show that the problem of finding redundant clauses is NP-complete, by encoding the boolean satisfiability (SAT) problem into it. So the worst-case running time is necessarily exponential.…”

Adaptive Pattern Matching on Binary Data

“…[3,14]. Such tree-based approaches guarantee that no constructor symbol is inspected twice, but doing so leads to exponential upper bounds on the automaton size.…”

“…However, since the optimization problem is NP-complete, [3] argues that heuristics should be employed to find near-optimal trees. In the same spirit, [14] also suggests several different heuristics to synthesize an adaptive traversal order that results in a tree automaton of small size. To further decrease the size of the automaton they generate a directed acyclic graph (DAG) automaton by sharing all isomorphic subtrees.…”

“…To further decrease the size of the automaton they generate a directed acyclic graph (DAG) automaton by sharing all isomorphic subtrees. Finally, [13] also examines several different match-compilation heuristics (including those of [3,14]) and measures their effects on different benchmarks. However, all these works heavily rely on being able to do a constructor-based decomposition of patterns, and to inspect terms in positions which are known statically.…”