Related papers: Formalization of simplification for context-free g…
Indexed languages are a generalization of context-free languages and form a proper subset of context-sensitive languages. We propose to generalize to indexed languages several well known characterizations of context-free languages: namely,…
A filtration of a formal language L by a sequence s maps L to the set of words formed by taking the letters of words of L indexed only by s. We consider the languages resulting from filtering by all arithmetic progressions. If L is regular,…
The paper demonstrates the non-closure of the family of unambiguous linear languages (that is, those defined by unambiguous linear context-free grammars) under complementation. To be precise, a particular unambiguous linear grammar is…
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…
We consider the class of groups whose word problem is poly-context-free; that is, an intersection of finitely many context-free languages. We show that any group which is virtually a finitely generated subgroup of a direct product of free…
This paper proposes a natural language translation method for machine-verifiable formal proofs that leverages the informalization (verbalization of formal language proof steps) and summarization capabilities of LLMs. For evaluation, it was…
We consider the problem of symbolic reachability analysis of higher-order context-free processes. These models are generalizations of the context-free processes (also called BPA processes) where each process manipulates a data structure…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
Formal languages let us define the textual representation of data with precision. Formal grammars, typically in the form of BNF-like productions, describe the language syntax, which is then annotated for syntax-directed translation and…
The algebraic properties of the combination of probabilistic choice and nondeterministic choice have long been a research topic in program semantics. This paper explains a formalization in the Coq proof assistant of a monad equipped with…
Our research is part of a wider project that aims to investigate and reason about the correctness of scheme-based source code transformations of Erlang programs. In order to formally reason about the definition of a programming language and…
In the context of interactive theorem provers based on a dependent type theory, automation tactics (dedicated decision procedures, call of automated solvers, ...) are often limited to goals which are exactly in some expected logical…
A common question when studying a class of context-free grammars is whether equivalence is decidable within this class. We answer this question positively for the class of Clark-congruential grammars, which are of interest to grammatical…
Termination is an important property of programs; notably required for programs formulated in proof assistants. It is a very active subject of research in the Turing-complete formalism of term rewriting systems, where many methods and tools…
We present an algorithm for synthesizing a context-free grammar encoding the language of valid program inputs from a set of input examples and blackbox access to the program. Our algorithm addresses shortcomings of existing grammar…
We propose a new approach for universal lossless text compression, based on grammar compression. In the literature, a target string $T$ has been compressed as a context-free grammar $G$ in Chomsky normal form satisfying $L(G) = \{T\}$. Such…
Traditionally, formal languages are defined as sets of words. More recently, the alternative coalgebraic or coinductive representation as infinite tries, i.e., prefix trees branching over the alphabet, has been used to obtain compact and…
Constraint logic grammars provide a powerful formalism for expressing complex logical descriptions of natural language phenomena in exact terms. Describing some of these phenomena may, however, require some form of graded distinctions which…
Context-free languages can be characterized in several ways. This article studies projective linearisations of languages of simple dependency trees, i.e., dependency trees in which a node can govern at most one node with a given syntactic…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…