Martin Berglund

Martin Berglund, Brink van der Merwe, Iain le Roux

Backtracking regular expression matchers are widely used due to their expressive power but may exhibit exponential worst-case matching time. Memoization provides a principled method for eliminating redundant computation and ensuring linear matching time, but full memoization is memory-intensive and impractical. We introduce the Minimum Feedback Node (MFN) memoization scheme, a selective memoization strategy based on computing a minimum feedback vertex set of an automaton. We establish relationships with existing memoization schemes and analyze their behaviour under both Thompson and Glushkov automaton constructions.

Martin Berglund, Brink van der Merwe, Sicheol Sung

Regular expressions with counting operations (c-regexes) offer a compact representation of repeating patterns by allowing numerical bounds to be added to subexpressions. Recent work introduced the counting-set data structure, which allows simultaneous updates of multiple counter values for efficient matching. However, this approach suffers from a performance bottleneck when counting-sets must be replicated due to the presence of branching transitions. We propose a sparse counting-set approach, which reduces the replication overhead by maintaining only essential counter values, thereby yielding a more efficient matching algorithm.

Martin Berglund, Willeke Martens, Brink van der Merwe

Many natural language processing systems operate over tokenizations of text to address the open-vocabulary problem. In this paper, we give and analyze an algorithm for the efficient construction of deterministic finite automata (DFA) designed to operate directly on tokenizations produced by the popular byte pair encoding (BPE) technique. This makes it possible to apply many existing techniques and algorithms to the tokenized case, such as pattern matching, equivalence checking of tokenization dictionaries, and composing tokenized languages in various ways. The construction preserves some key properties of the automaton, and we use this to establish asymptotic bounds on the state complexity of the automata that result. Finally, we demonstrate how to construct an input-deterministic (subsequential) string-to-string transducer which precisely describes the relationship between strings and their correct tokenizations.