Notes from COSC 341/2 1/27/2015

Regular expressions

A regular expression (RE) is one of

1. character (from the alphabet)

2. ε

3. RE1 ∙ RE2     	// concatenation -- RE1 followed by RE2
       		// where RE1 and RE2 are regular expressions
       		// the ∙ symbol may be implied (like multiplication symbol)
       	 

4. RE1 | RE2	// or, alternative -- RE1  or  RE2
       	 

5. RE*		// Kleene closure -- 0 or more occurences of RE
           

• Binary operators: ∙ and |
• Unary postfix operator: *

Finite Automata

A vertex represents a state. An edge represents a transition.
The label on an edge is the (input) character that causes a transition from initial state to target state.

If a transition is labelled with ε, then a transition from start state to destination state is triggered by an input string of 0 length.

• A deterministic finite automaton is one where there is no choice about which transition will apply. From a given state, with a given input, only one transition is possible.
• A nondeterministic finite automaton is one where there is a choice about which transition applies. From a given state, with a given input, there may be multiple transitions that qualify.

Example RE --> NFA

NFA -> DFA conversion

Algorithm
1. For every state in NFA, determine all reachable states for every input symbol.
2. The set of reachable states forms a single state in the DFA.
3. Find reachable states for each new DFA state until no more new states can be found.