Question

For every regular expression E there is a deterministic finite state automaton M such that L(E)=L(M) where L(E) is the language represented by the regular expression E

true
false

Answer 1

The claim that for every regular expression there exists a deterministic finite automaton with equivalent language is true. The statement is true

Step-by-step explanation:

The statement that for every regular expression E there is a deterministic finite automaton M such that L(E)=L(M) where L(E) is the language represented by the regular expression E is true. This foundational concept in the theory of computation and formal languages is known as the equivalence of regular expressions and deterministic finite automata (DFAs).

Essentially, for any regular expression, you can construct a DFA that recognizes the same language, and conversely, for any DFA, there is a regular expression that describes the language it recognizes. The construction of a DFA from a regular expression involves creating non-deterministic finite automata (NFA) first and then converting this NFA to an equivalent DFA using the subset construction method, a process commonly known as NFA to DFA conversion.

To demonstrate with an example, consider a simple regular expression 'ab'. We can construct an NFA that accepts this expression and then apply the subset construction to obtain a DFA which consists of a start state, a state for when 'a' is consumed, and a final state after 'b' is consumed. This DFA will accept the string 'ab' and only 'ab', just like the regular expression.