Related papers: Formal Languages via Theories over Strings
Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive…
Term algebras are important objects in computer science and are correspondingly well-studied. A natural generalization is to quotient these algebras by finitely many ground term equations, obtaining what we call almost free algebras. One of…
We investigate the complexity of satisfiability for finite-variable fragments of propositional dynamic logics. We consider three formalisms belonging to three representative complexity classes, broadly understood,---regular PDL, which is…
Several queries and scores have recently been proposed to explain individual predictions over ML models. Given the need for flexible, reliable, and easy-to-apply interpretability methods for ML models, we foresee the need for developing…
We study formal languages which are capable of fully expressing quantitative probabilistic reasoning and do-calculus reasoning for causal effects, from a computational complexity perspective. We focus on satisfiability problems whose…
Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. Regular constraints restrict valid substitutions of…
In this article we undertake a study of extension complexity from the perspective of formal languages. We define a natural way to associate a family of polytopes with binary languages. This allows us to define the notion of extension…
Recent work shows superior performance when using large language models (LLMs) as formalizers instead of as end-to-end solvers for symbolic reasoning problems. Given the problem description, the LLM generates a formal program that derives a…
Lexical semantics theories differ in advocating that the meaning of words is represented as an inference graph, a feature mapping or a vector space, thus raising the question: is it the case that one of these approaches is superior to the…
We investigate abstract model theoretic properties which holds for models in which a truth or satisfaction predicate for a sublanguage of the signature is definable. We analyse in which cases those properties in fact ensure the definability…
Models of a generalized nondeterminism are defined by limitations on nonde- terministic behavior of a computing device. A regular realizability problem is a problem of verifying existence of a special sort word in a regular language. These…
We study expressibility in infinitary languages of the modal operators associated with satisfiability of sentences of these languages in submodels and extensions of models. We give a syntactic criterion for expressibility in finitary…
The separability problem for word languages of a class $\mathcal{C}$ by languages of a class $\mathcal{S}$ asks, for two given languages $I$ and $E$ from $\mathcal{C}$, whether there exists a language $S$ from $\mathcal{S}$ that includes…
We consider first-order logic over the subword ordering on finite words, where each word is available as a constant. Our first result is that the $\Sigma_1$ theory is undecidable (already over two letters). We investigate the decidability…
Human beings possess the most sophisticated computational machinery in the known universe. We can understand language of rich descriptive power, and communicate in the same environment with astonishing clarity. Two of the many contributors…
Languages vary widely in how meanings map to word forms. These mappings have been found to support efficient communication; however, this theory does not account for systematic relations within word forms. We examine how a restricted set of…
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.…
We consider decision problems for relations over finite and infinite words defined by finite automata. We prove that the equivalence problem for binary deterministic rational relations over infinite words is undecidable in contrast to the…
Written language is a complex communication signal capable of conveying information encoded in the form of ordered sequences of words. Beyond the local order ruled by grammar, semantic and thematic structures affect long-range patterns in…
Sequence theories are an extension of theories of strings with an infinite alphabet of letters, together with a corresponding alphabet theory (e.g. linear integer arithmetic). Sequences are natural abstractions of extendable arrays, which…