The.Algorithm.Design.Manual.Springer-Verlag.1998

Finite State Machine Minimization
Section .
XTango (see Section ) includes a simulation of a DFA. Many of the other animations (but not this
one) are interesting and quite informative to watch.
FLAP (Formal Languages and Automata Package) is a tool by Susan Rodger for drawing and simulating
finite automata, pushdown automata, and Turing machines. Using FLAP, one can draw a graphical
representation (transition diagram) of an automaton, edit it, and simulate the automaton on some input.
FLAP was developed in C++ for X-Windows. See http://www.cs.duke.edu:80/ rodger/tools/tools.html.
Notes: Aho [Aho90] provides a good survey on algorithms for pattern matching, and a particularly clear
exposition for the case where the patterns are regular expressions. The technique for regular expression
pattern matching with -moves is due to Thompson [Tho68]. Other expositions on finite automaton
pattern matching include [AHU74].
Hopcroft [Hop71] gave an optimal algorithm for minimizing the number of states in DFAs. The
derivatives method of constructing a finite state machine from a regular expression is due to Brzozowski
[Brz64] and has been expanded upon in [BS86]. Expositions on the derivatives method includes Conway
[]. Testing the equivalence of two nondeterministic finite state machines is PSPACE-complete [SM73].
Related Problems: Satisfiability (see page ). string matching (see page ).
Next: Longest Common Substring Up: Set and String Problems Previous: Cryptography
Algorithms
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