Related papers: Non-Deterministic Kleene Coalgebras
First we identify the free algebras of the class of algebras of binary relations equipped with the composition and domain operations. Elements of the free algebras are pointed labelled finite rooted trees. Then we extend to the analogous…
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…
Regular expressions are widely used in software. Various regular expression engines support different combinations of extensions to classical regular constructs such as Kleene star, concatenation, nondeterministic choice (union in terms of…
Coalgebras generalize various kinds of dynamical systems occuring in mathematics and computer science. Examples of systems that can be modeled as coalgebras include automata and Markov chains. We will present a coalgebraic representation of…
Techniques are presented for defining models of computational linguistics theories. The methods of generalized diagrams that were developed by this author for modeling artificial intelligence planning and reasoning are shown to be…
I present the most fundamental features of an implemented system designed to manipulate representations of regular languages. The system is structured into two layers, allowing regular languages to be represented in an increasingly compact,…
Relational verification encompasses information flow security, regression verification, translation validation for compilers, and more. Effective alignment of the programs and computations to be related facilitates use of simpler relational…
Brzozowski derivatives of a regular expression are developed for constructing deterministic automata from the given regular expression in the algebraic way. In this paper,some lemmas of the regular expressions are discussed and the regular…
We investigate the equational theory of Kleene algebra terms with variable complements -- (language) complement where it applies only to variables -- w.r.t. languages. While the equational theory w.r.t. languages coincides with the language…
This paper proposes an alternative language for expressing results of the algorithmic theory of randomness. The language is more precise in that it does not involve unspecified additive or multiplicative constants, making mathematical…
Abstract numeration systems encode natural numbers using radix ordered words of an infinite regular language and linear recurrence sequences play a key role in their valuation. Sequence automata, which are deterministic finite automata with…
$\omega$-clones are multi-sorted structures that naturally emerge as algebras for infinite trees, just as $\omega$-semigroups are convenient algebras for infinite words. In the algebraic theory of languages, one hopes that a language is…
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.
Kleene Algebra (KA) is a useful tool for proving that two programs are equivalent. Because KA's equational theory is decidable, it integrates well with interactive theorem provers. This raises the question: which equations can we (not)…
We study a categorical generalisation of tree automata, as $\Sigma$-algebras for a fixed endofunctor $\Sigma$ endowed with initial and final states. Under mild assumptions about the base category, we present a general minimisation algorithm…
We propose the first steps in the development of a tool to automate the translation of Redex models into a (hopefully) semantically equivalent model in Coq, and to provide tactics to help in the certification of fundamental properties of…
Guarded Kleene Algebra with Tests (GKAT) is an efficient fragment of KAT, as it allows for almost linear decidability of equivalence. In this paper, we study the (co)algebraic properties of GKAT. Our initial focus is on the fragment that…
Kleene algebras with tests (KATs) offer sound, complete, and decidable equational reasoning about regularly structured programs. Interest in KATs has increased greatly since NetKAT demonstrated how well extensions of KATs with…
$KS$-algebra consists of expressions constructed with four kinds operations, the minimum, maximum, difference and additively homogeneous generalized means. Five families of $Z$-classifiers are investigated on binary classification tasks…
This article introduces an innovative architecture designed to declaratively combine Large Language Models (LLMs) with shared histories, and triggers to identify the most appropriate LLM for a given task. Our approach is general and…