Finite Automata in compiler design
- 1. In the theory of computation, a branch of theoretical computer science, a deterministic finite automaton (DFA)— also known as a deterministic finite acceptor (DFA) and a deterministic finite state machine (DFSM)—is a finite-state machine that accepts and rejects strings of symbols and only produces a unique computation (or run) of the automaton for each input string.Deterministic refers to the uniqueness of the computation. In search of the simplest models to capture finite-state machines, McCulloch and Pitts were among the first researchers to introduce a concept similar to finite automata in 1943.
- 2. Finite Automata (a) Nondeterministic finite automata (NFA) have no restrictions on the labels of their edges. A symbol can label several edges out of the same state, and E, the empty string, is a possible label. (b) Deterministic finite automata (DFA) have, for each state, and for each symbol of its input alphabet exactly one edge with that symbol leaving that state.
- 3. Nondeterministic Finite Automata 1. A finite set of states S. 2. A set of input symbols C, the input alphabet. We assume that E, which stands for the empty string, is never a member of C. 3. A transition function that gives, for each state, and for each symbol in C U (E) a set of next states. 4. A state so from S that is distinguished as the start state (or initial state). 5. A set of states F, a subset of S, that is distinguished as the accepting states (or final states).
- 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.
- 7. Deterministic Finite Automata A deterministic finite automaton (DFA) is a special case of an NFA where:
- 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