Baiyu Li

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 prove that n^n^-^2 is a tight upper bound for prefix-free regular languages. We present properties of the syntactic semigroups of suffix-, bifix-, and factor-free regular languages, conjecture tight upper bounds on their size to be (n-1)^n^-^2+(n-2), (n-1)^n^-^3+(n-2)^n^-^3+(n-3)2^n^-^3, and (n-1)^n^-^3+(n-3)2^n^-^3+1, respectively, and exhibit languages with these syntactic complexities.

Syntactic Complexity Of R- And J-Trivial Regular Languages

The syntactic complexity of a subclass of the class of regular languages is the maximal cardinality of syntactic semigroups of languages in that class, taken as a function of the state complexity n of these languages. We prove that n! and ⌊e(n − 1)⌋. are tight upper bounds for the syntactic complexity of ℛ- and 𝒥-trivial regular languages, respectively.

Syntactic Complexity of \({\mathcal R}\)- and \({\mathcal J}\)-Trivial Regular Languages

The syntactic complexity of a subclass of the class of regular languages is the maximal cardinality of syntactic semigroups of languages in that class, taken as a function of the state complexity n of these languages. We prove that n! and \(\lfloor e(n-1)! \rfloor\) are tight upper bounds for the syntactic complexity of \({\mathcal R}\)- and \({\mathcal J}\)-trivial regular languages, respectively.

ON THE COMPLEXITY OF THE EVALUATION OF TRANSIENT EXTENSIONS OF BOOLEAN FUNCTIONS

Electronic version of an article published as International Journal of Foundations of Computer Science, 23(01), 2012, 21–35. http://dx.doi.org/10.1142/S0129054112400023

Syntactic complexity of Prefix-, Suffix-, and Bifix-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-, 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 suffix- and bifix-free regular languages, and conjecture tight upper bounds on their size.

On the Complexity of the Evaluation of Transient Extensions of Boolean Functions

Transient algebra is a multi-valued algebra for hazard detection in gate circuits. Sequences of alternating 0s and 1s, called transients, represent signal values, and gates are modeled by extensions of boolean functions to transients. Formulas for computing the output transient of a gate from the input transients are known for NOT, AND, OR} and XOR gates and their complements, but, in general, even the problem of deciding whether the length of the output transient exceeds a given bound is NP-complete. We propose a method of evaluating extensions of general boolean functions. We introduce and study a class of functions with the following property: Instead of evaluating an extension of a boolean function on a given set of transients, it is possible to get the same value by using transients derived from the given ones, but having length at most 3. We prove that all functions of three variables, as well as certain other functions, have this property, and can be efficiently evaluated.