Syntactic Complexity of Prefix-, Suffix-, and Bifix-Free Regular Languages
نویسندگان
چکیده
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 prefix-, suffix-, and bifix-free regular languages. We prove that nn−2 is a tight upper bound for prefix-free regular languages. We present properties of the syntactic semigroups of suffixand bifix-free regular languages, and conjecture tight upper bounds on their size.
منابع مشابه
Syntactic complexity of prefix-, suffix-, bifix-, and factor-free 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 prefix-, suffix-, bifix-, and factor-free regular languages. We...
متن کاملComplexity 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 کاملQuotient Complexity of Bifix-, Factor-, and Subword-Free Regular Languages
A language L is prefix-free if, whenever words u and v are in L and u is a prefix of v, then u = v. Suffix-, factor-, and subword-free languages are defined similarly, where “subword” means “subsequence”. A language is bifix-free if it is both prefixand suffix-free. We study the quotient complexity, more commonly known as state complexity, of operations in the classes of bifix-, factor-, and su...
متن کاملSyntactic Complexity of Bifix-Free Languages
We study the properties of syntactic monoids of bifix-free regular languages. In particular, we solve an open problem concerning syntactic complexity: We prove that the car-dinality of the syntactic semigroup of a bifix-free language with state complexity n is at most (n−1) n−3 +(n−2) n−3 +(n−3)2 n−3 for n 6. The main proof uses a large construction with the method of injective function. Since ...
متن کاملCS – 2008 – 06 Continuous Languages
A language is prefix-continuous if it satisfies the condition that, if a word w and its prefix u are in the language, then so is every prefix of w that has u as a prefix. Prefix-continuous languages include prefix-closed languages at one end of the spectrum, and prefix-free languages, which include prefix codes, at the other. In a similar way, we define suffix-, bifix-, factor-, and subword-con...
متن کامل