Exact string matching Rhys Price Jones Anne Haake Week 2: Bioinformatics Computing I continued

Wild Cards How do you adapt the algorithm to accommodate ? wild cards in the pattern P? (? matches any SINGLE character). Biological relevance How do you adapt the algorithm to accommodate Σ * wild cards in the pattern P? (Σ * matches zero or more characters) Biological relevance

Rabin-Karp algorithm Illustrate with nucleotide sequences For long sequences, need to do modular arithmetic. Worst case analysis is still O(nm) since all the potential hits may need to be checked out. When does worst case occur? Expected case is O(n+m)

Rabin-Karp and Wild Cards What happens if you have a ? wildcard in the search pattern? What about a Σ * wildcard?

Regular Expressions Example –AC(T+A)*CA Recursive definition –terminal, or –r 1 +r 2 or r 1 r 2 or r* –where r, r 1, r 2 are reg.exps. Regular expressions and Perl

Finite State Automata Definition Q, , , q 0, F Examples Example of string-matching automaton Give algorithm finite-automaton-matcher Discuss correctness

Finite State Automata and Regular Expressions It can be shown that for any regular expression, you can build a finite state automaton that recognizes exactly those strings containing a substring matching the regular expression. It can be shown that for any finite state automaton M, you can write a regular expression for the set of strings recognized by M.

String matching with finite automata. Blackboard illustration