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Term rewriting systems have a simple syntax and semantics and facilitate proofs of correctness. However, they are not as popular in industry or academia as imperative languages. We define a term rewriting based abstract programming language…
Digital learning platforms enable students to learn on a flexible and individual schedule as well as providing instant feedback mechanisms. The field of STEM education requires students to solve numerous training exercises to grasp…
This paper describes a first step towards the definition of an abstract machine for linguistic formalisms that are based on typed feature structures, such as HPSG. The core design of the abstract machine is given in detail, including the…
An attractive mechanism to specify global constraints in rostering and other domains is via formal languages. For instance, the Regular and Grammar constraints specify constraints in terms of the languages accepted by an automaton and a…
We consider grammar-restricted exact learning of formulas and terms in finite variable logics. We propose a novel and versatile automata-theoretic technique for solving such problems. We first show results for learning formulas that…
This work is a survey of the main results reported for the degree of extension of two models defining non-regular languages, namely the context-free grammar and the extended automaton over groups. More precisely, we recall the main results…
The representation of numbers by product states in quantum mechanics can be extended to the representation of words and word sequences in languages by product states. This can be used to study quantum systems that generate text that has…
A fundamental theme in automata theory is regular languages of words and trees, and their many equivalent definitions. Salvati has proposed a generalization to regular languages of simply typed $\lambda$-terms, defined using denotational…
Logical rules are a popular knowledge representation language in many domains, representing background knowledge and encoding information that can be derived from given facts in a compact form. However, rule formulation is a complex process…
Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
An object--oriented approach to create a natural language understanding system is considered. The understanding program is a formal system built on the base of predicative calculus. Horn's clauses are used as well--formed formulas. An…
Information, stored or transmitted in digital form, is often structured. Individual data records are usually represented as hierarchies of their elements. Together, records form larger structures. Information processing applications have to…
What can large language models learn? By definition, language models (LM) are distributions over strings. Therefore, an intuitive way of addressing the above question is to formalize it as a matter of learnability of classes of…
The goal of the present paper is to provide a systematic and comprehensive study of rational stochastic languages over a semiring K \in {Q, Q +, R, R+}. A rational stochastic language is a probability distribution over a free monoid…
Linguistic evaluations of how well LMs generalize to produce or understand language often implicitly take for granted that natural languages are generated by symbolic rules. According to this perspective, grammaticality is determined by…
We consider some questions about formal languages that arise when inverses of letters, words and languages are defined. The reduced representation of a language over the free monoid is its unique equivalent representation in the free group.…
This paper develops a free energy theory from physics including the variational principles for automata and languages and also provides algorithms to compute the energy as well as efficient algorithms for estimating the nondeterminism in a…
Executing computer programs described in natural language has long been a pursuit of computer science. With the advent of enhanced natural language understanding capabilities exhibited by large language models (LLMs), the path toward this…
Despite significant advancements in the conception of (formal) integrated development environments, applying formal methods in software industry is still perceived as a difficult task. To make the task easier, providing tools that help…