A Note on Definition of Finite Automata
Han Guang-hu · Computer and Information Technology · 2015
A general definition of finite automata, M=(Q,Σ,R,q0,F), is proposed, where R 哿(Q ×(Σ ∪{e})) ×Q, in particular, M is a deterministic finite automaton if R:Q×Σ→Q. This definition uniformly describe deterministic finite automata, nondeterministic finite automata, nondeterministic finite automata with e-transition and partial automata. Based on the general definition, the equivalence between deterministic finite automata and nondeterministic finite automata, as well as the closure property of class of regular languages under concatenation operation and Kleene closure(*) operation are proved. So the definition is theoretically complete.