Finite Automata in compiler design
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This document discusses deterministic finite automata (DFAs) and nondeterministic finite automata (NFAs). It defines DFAs and NFAs, describes their components and representations using transition graphs and tables. It also discusses converting NFAs to equivalent DFAs, which is important for implementing pattern matching software using finite state machines.
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- 4. The transition graph for an NFA recognizing the language of regular expression (aJb)*abb is shown in Fig.
- 5. Transition Tables We can also represent an NFA by a transition table, whose rows correspond to states, and whose columns correspond to the input symbols and c. The entry for a given state and input is the value of the transition function applied to those arguments. If the transition function has no information about that state-input pair, we put Q) in the table for the pair
- 6. The transition table for the NFA of Fig.
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- 8. DFA 1. There are no moves on input E, and 2. For each state s and input symbol a, there is exactly one edge out of s labeled a. If we are using a transition table to represent a DFA, then each entry is a single state. we may therefore represent this state without the curly braces that we use to form sets
- 9. In Fig. 3.28 we see the transition graph of a DFA accepting the language (alb)*abb
- 10. From Regular Expressions to Automata The regular expression is the notation of choice for describing lexical analyzers and other pattern-processing software. How- ever, implementation of that software requires the simulation of a DFA, or perhaps simulation of an NFA. Because an NFA often has a choice of move on an input symbol (as Fig. 3.24 does on input a from state 0) or on e (as Fig. 3.26 does from state 0), or even a choice of making a transition on E: or on a real input symbol, its simulation is less straightforward than for a DFA. Thus often it is important to convert an NFA to a DFA that accepts the same language.
- 11. Conversion of an NFA to a DFA shows another NFA accepting (a1 b) *abb