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We consider equivalence and containment problems for word transductions. These problems are known to be undecidable when the transductions are relations between words realized by non-deterministic transducers, and become decidable when…
Symbolic Finite Automata and Register Automata are two orthogonal extensions of finite automata motivated by real-world problems where data may have unbounded domains. These automata address a demand for a model over large or infinite…
The paper introduces a new lossless, highly robust compression algorithm that similar with LZW algorithm, yet the algorithm discards dictionary processing and uses irregular sequences with massive, random information instead. Then the paper…
We study 4 problems in string matching, namely, regular expression matching, approximate regular expression matching, string edit distance, and subsequence indexing, on a standard word RAM model of computation that allows logarithmic-sized…
Symbolic execution is a powerful technique for program analysis. However, it has many limitations in practical applicability: the path explosion problem encumbers scalability, the need for language-specific implementation, the inability to…
We discuss inequalities holding between the vocabulary size, i.e., the number of distinct nonterminal symbols in a grammar-based compression for a string, and the excess length of the respective universal code, i.e., the code-based analog…
Traditionally, finite automata theory has been used as a framework for the representation of possibly infinite sets of strings. In this work, we introduce the notion of second-order finite automata, a formalism that combines finite automata…
This paper introduces to the calculus of regular expressions a replace operator, ->, and defines a set of replacement expressions that concisely encode several alternate variations of the operation. The basic case is unconditional…
Several abstract machines that operate on symbolic input alphabets have been proposed in the last decade, for example, symbolic automata or lattice automata. Applications of these types of automata include software security analysis and…
Solutions of symbolic regression problems are expressions that are composed of input variables and operators from a finite set of function symbols. One measure for evaluating symbolic regression algorithms is their ability to recover…
The aim of this paper is to establish some new inequalities similar to the Ostrowski's inequalities which are more generalized than the inequalities of Dragomir and Cerone. The current article obtains bounds for the deviation of a function…
We use symbolic expressions for traces of positive integer powers of a Hermitian operator (or, equivalently, coefficients of corresponding characteristic polynomial) to find solutions for the problems as follows: Factorization of…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function so that along the iterations the objective function decreases. Such a simple principle allows to solve a large…
We study the universality and inclusion problems for register automata over equality data. We show that the universality and the inclusion problems can be solved with 2-EXPTIME complexity when the input automata are without guessing and…
Satisfiability of word equations is an important problem in the intersection of formal languages and algebra: Given two sequences consisting of letters and variables we are to decide whether there is a substitution for the variables that…
We provide the solution to the normal ordering problem for powers and exponentials of two classes of operators. The first one consists of boson strings and more generally homogeneous polynomials, while the second one treats operators linear…
We consider (logical) reasoning for regular expressions with lookahead (REwLA). In this paper, we give an axiomatic characterization for both the (match-)language equivalence and the largest substitution-closed equivalence that is sound for…
Extracting dense representations for terms and phrases is a task of great importance for knowledge discovery platforms targeting highly-technical fields. Dense representations are used as features for downstream components and have multiple…
A new method of deriving comparative statics information using generalized compensated derivatives is presented which yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. More generally,…
In the computational-mechanics structural analysis of one-dimensional cellular automata the following automata-theoretic analogue of the \emph{change-point problem} from time series analysis arises: \emph{Given a string $\sigma$ and a…