Reversal of regular languages and state complexity
نویسنده
چکیده
We study the state complexity of languages that can be obtained as reversals of regular languages represented by deterministic finite automata. We show that the state complexity of the reversal of a regular language with state complexity n is between logn and 2. We first prove that the upper bound is tight in the ternary case. Then we present binary languages reaching this upper bound on the reversal. We also obtain some other partial results in the binary case.
منابع مشابه
Complexity of regular bifix-free languages
We study descriptive complexity properties of the class of regular bifix-free languages, which is the intersection of prefix-free and suffix-free regular languages. We show that there exist a single ternary universal (stream of) bifix-free languages that meet all the bounds for the state complexity basic operations (Boolean operations, product, star, and reversal). This is in contrast with suff...
متن کاملTowards a Theory of Complexity of Regular Languages
We survey recent results concerning the complexity of regular languages represented by their minimal deterministic finite automata. In addition to the quotient complexity of the language – which is the number of its (left) quotients, and is the same as its state complexity – we also consider the size of its syntactic semigroup and the quotient complexity of its atoms – basic components of every...
متن کاملState Complexity of Basic Operations on Non-returning Regular Languages
We consider the state complexity of basic operations on non-returning regular languages. For a non-returning minimal DFA, the start state does not have any in-transitions. We establish the precise state complexity of four Boolean operations (union, intersection, difference, symmetric difference), catenation, reverse, and Kleene-star for non-returning regular languages. Our results are usually s...
متن کاملTechnical Report No. 2007-534 State Complexity of Basic Operations on Suffix-Free Regular Languages
We investigate the state complexity of basic operations for suffix-free regular languages. The state complexity of an operation for regular languages is the number of states that are necessary and sufficient in the worst-case for the minimal deterministic finite-state automaton that accepts the language obtained from the operation. We establish the precise state complexity of catenation, Kleene...
متن کاملSyntactic Complexity of R- and J-Trivial Regular Languages
The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of the class of regular languages is the maximal syntactic complexity of languages in that class, taken as a function of the state complexity n of these languages. We study the syntactic complexity of Rand J -trivial regular languages, and prove that n! and ⌊e(n −...
متن کامل