A very fast substring search algorithm
Communications of the ACM
Average running time of the Boyer-Moore-Horspool algorithm
Theoretical Computer Science - Selected papers of the Combinatorial Pattern Matching School
Analysis of Boyer-Moore-Horspool string-matching heuristic
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
Analysis of Boyer-Moore-type string searching algorithms
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
A fast string searching algorithm
Communications of the ACM
The Boyer-Moore-Horspool heuristic with Markovian input
Random Structures & Algorithms
Flexible pattern matching in strings: practical on-line search algorithms for texts and biological sequences
Probabilistic Arithmetic Automata and Their Application to Pattern Matching Statistics
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
Fast and Adaptive Variable Order Markov Chain Construction
WABI '08 Proceedings of the 8th international workshop on Algorithms in Bioinformatics
Computing Alignment Seed Sensitivity with Probabilistic Arithmetic Automata
WABI '08 Proceedings of the 8th international workshop on Algorithms in Bioinformatics
Efficient exact motif discovery
Bioinformatics
Probabilistic Arithmetic Automata and Their Applications
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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We define deterministic arithmetic automata (DAAs) and connect them to a framework called probabilistic arithmetic automata (PAAs) [9]. We use DAAs and PAAs to compute the entire exact probability distribution (in contrast to, e.g., asymptotic expectation and variance) of the number $X^p_\ell$ of text characters accessed by the Horspool or Sunday pattern matching algorithms when matching a fixed pattern p against a random text of length ℓ. The random text model can be quite general, from simple uniform models to higher-order Markov models or hidden Markov models (HMMs). We develop several alternative constructions with different state spaces of the automata, leading to alternative time and space complexities for the computations. To our knowledge, this is the first time that suffix-based pattern matching algorithms are analyzed exactly. We present (perhaps surprising) exemplary results on short patterns and moderate text lengths. Our results easily generalize to any search-window based pattern matching algorithm.