Nested Counters in Bit-Parallel String Matching

Many algorithms, e.g. in the field of string matching, are based on handling many counters, which can be performed in parallel, even on a sequential machine, using bit-parallelism. The recently presented technique of nested counters (Matryoshka counters) [1] is to handle small counters most of the time, and refer to larger counters periodically, when the small counters may get full, to prevent overflow. In this work, we present several non-trivial applications of Matryoshka counters in string matching algorithms, improving their worstor average-case time complexities. The set of problems comprises (δ, α)-matching, matching with k insertions, episode matching, and matching under Levenshtein