Related papers: A proof Procedure for Testing Membership in Regula…
This paper presents an algorithm, Voted Kernel Regularization , that provides the flexibility of using potentially very complex kernel functions such as predictors based on much higher-degree polynomial kernels, while benefitting from…
A new technique is presented to prove non-termination of term rewriting. The basic idea is to find a non-empty regular language of terms that is closed under rewriting and does not contain normal forms. It is automated by representing the…
Mathematical theorem proving is an important testbed for large language models' deep and abstract reasoning capability. This paper focuses on improving LLMs' ability to write proofs in formal languages that permit automated proof…
This paper presents the main features of a system that aims to transform regular expressions into shorter equivalent expressions. The system is also capable of computing other operations useful for simplification, such as checking the…
Fast matching of regular expressions with bounded repetition, aka counting, such as (ab){50,100}, i.e., matching linear in the length of the text and independent of the repetition bounds, has been an open problem for at least two decades.…
Recently, the problem of obtaining a short regular expression equivalent to a given finite automaton has been intensively investigated. Algorithms for converting finite automata to regular expressions have an exponential blow-up in the…
Existing support for regular expressions in automated test generation or verification tools is lacking. Common aspects of regular expression engines found in mainstream programming languages, such as backreferences or greedy matching, are…
Proving programs terminating is a fundamental computer science challenge. Recent research has produced powerful tools that can check a wide range of programs for termination. The analog for probabilistic programs, namely termination with…
The demonstrated code-understanding capability of LLMs raises the question of whether they can be used for automated program verification, a task that demands high-level abstract reasoning about program properties that is challenging for…
This article presents a novel framework to provide Formal Languages and Automata Theory students design support for the development of regular expressions. This framework includes a design recipe for regular expressions and a customized…
Regular expressions with backreferences (regex, for short), as supported by most modern libraries for regular expression matching, have an NP-complete matching problem. We define a complexity parameter of regex, called active variable…
We describe a method for proving non-looping non-termination, that is, of term rewriting systems that do not admit looping reductions. As certificates of non-termination, we employ regular (tree) automata.
We investigate two problems for a class C of regular word languages. The C-membership problem asks for an algorithm to decide whether an input language belongs to C. The C-separation problem asks for an algorithm that, given as input two…
Given a regular expression $R$ and a string $Q$, the regular expression parsing problem is to determine if $Q$ matches $R$ and if so, determine how it matches, e.g., by a mapping of the characters of $Q$ to the characters in $R$. Regular…
An algorithm to decide the emptiness of a regular type expression with set operators given a set of parameterised type definitions is presented. The algorithm can also be used to decide the equivalence of two regular type expressions and…
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…
We study the class of languages that have membership proofs which can be verified by real-time finite-state machines using only a constant number of random bits, regardless of the size of their inputs. Since any further restriction on the…
Scalable and automatic formal verification for concurrent systems is always demanding. In this paper, we propose a verification framework to support automated compositional reasoning for concurrent programs with shared variables. Our…
The proofs first generated by automated theorem provers are far from optimal by any measure of simplicity. In this paper I describe a technique for simplifying automated proofs. Hopefully this discussion will stimulate interest in the…
This paper proposes an algorithm for computing regularized solutions to linear rational expectations models. The algorithm allows for regularization cross-sectionally as well as across frequencies. A variety of numerical examples illustrate…