Related papers: Symbolic Solving of Extended Regular Expression In…
Symmetry reduction is a well-known approach for alleviating the state explosion problem in model checking. Automatically identifying symmetries in concurrent systems, however, is computationally expensive. We propose a symbolic framework…
This article proposes a convenient tool for decoding the output of neural networks trained by Connectionist Temporal Classification (CTC) for handwritten text recognition. We use regular expressions to describe the complex structures…
In this paper, we consider solving a class of nonconvex and nonsmooth problems frequently appearing in signal processing and machine learning research. The traditional alternating direction method of multipliers encounters troubles in both…
Most modern libraries for regular expression matching allow back-references (i.e., repetition operators) that substantially increase expressive power, but also lead to intractability. In order to find a better balance between expressiveness…
In this chapter we discuss the problem of enumerating distinct regular expressions by size and the regular languages they represent. We discuss various notions of the size of a regular expression that appear in the literature and their…
The traditional methods for data compression are typically based on the symbol-level statistics, with the information source modeled as a long sequence of i.i.d. random variables or a stochastic process, thus establishing the fundamental…
Case split is a core proof rule in current decision procedures for the theory of string constraints. Its use is the primary cause of the state space explosion in string constraint solving, since it is the only rule that creates branches in…
We consider a regularization concept for the solution of ill--posed operator equations, where the operator is composed of a continuous and a discontinuous operator. A particular application is level set regularization, where we develop a…
Symbolic automata are finite state automata that support potentially infinite alphabets, such as the set of rational numbers, generally applied to regular expressions/languages over finite words. In symbolic automata (or automata modulo…
We consider forkable regular expressions, which enrich regular expressions with a fork operator, to establish a formal basis for static and dynamic analysis of the communication behavior of concurrent programs. We define a novel…
In the article we propose a general scheme for solutions of some approximation problems under a rather general setting. We illustrate the application of the proposed scheme by a series of examples, in particular we show that many results in…
Generalized Zeckendorf decompositions are expansions of integers as sums of elements of solutions to recurrence relations. The simplest cases are base-$b$ expansions, and the standard Zeckendorf decomposition uses the Fibonacci sequence.…
Mathematical notation makes up a large portion of STEM literature, yet finding semantic representations for formulae remains a challenging problem. Because mathematical notation is precise, and its meaning changes significantly with small…
Mixed-integer mathematical programs are among the most commonly used models for a wide set of problems in Operations Research and related fields. However, there is still very little known about what can be expressed by small mixed-integer…
When neural networks are used to solve differential equations, they usually produce solutions in the form of black-box functions that are not directly mathematically interpretable. We introduce a method for generating symbolic expressions…
Partial derivatives of regular expressions, introduced by Antimirov, define an elegant algorithm for generating equivalent non-deterministic finite automata (NFA) with a limited number of states. Here we focus on runtime verification (RV)…
We present a method to simplify expressions in the context of an equational theory. The basic ideas and concepts of the method have been presented previously elsewhere but here we tackle the difficult task of making it efficient in…
We introduce Exhaustive Symbolic Integration (ESI), a method that enumerates all symbolic functions up to a given complexity $k$ within a specified operator basis and determines which admit closed-form antiderivatives within the same class.…
We study the succinctness of the complement and intersection of regular expressions. In particular, we show that when constructing a regular expression defining the complement of a given regular expression, a double exponential size…
Generalization problems in languages with binders involve computing the most common structure between expressions while respecting bound variable renaming and freshness constraints. These problems often lack a least general solution.…