Search results
Results from the WOW.Com Content Network
The Myhill–Nerode theorem may be used to show that a language is regular by proving that the number of equivalence classes of is finite. This may be done by an exhaustive case analysis in which, beginning from the empty string , distinguishing extensions are used to find additional equivalence classes until no more can be found.
The converse is not true: for example, the language consisting of all strings having the same number of a's as b's is context-free but not regular. To prove that a language is not regular, one often uses the Myhill–Nerode theorem and the pumping lemma.
This string is in exactly when = and thus is not regular by the Myhill–Nerode theorem. The Myhill–Nerode theorem provides a test that exactly characterizes regular languages. The typical method for proving that a language is regular is to construct either a finite-state machine or a regular expression for the language.
The state of a deterministic finite automaton = (,,,,) is unreachable if no string in exists for which = (,).In this definition, is the set of states, is the set of input symbols, is the transition function (mapping a state and an input symbol to a set of states), is its extension to strings (also known as extended transition function), is the initial state, and is the set of accepting (also ...
The study of linear bounded automata led to the Myhill–Nerode theorem, [8] ... A familiar example of a machine recognizing a language is an electronic lock, ...
The Myhill–Nerode theorem for tree automata states that the following three statements are equivalent: [14] L is a recognizable tree language; L is the union of some equivalence classes of a congruence of finite index; the relation ≡ L is a congruence of finite index
The Myhill–Nerode theorem states: a language is regular if and only if the family of quotients {|} is finite, or equivalently, the left syntactic equivalence has finite index (meaning it partitions into finitely many equivalence classes).
Myhill–Nerode theorem (formal languages) No free lunch in search and optimization (computational complexity theory) PCP theorem (computational complexity theory)