Related papers: Formalization of simplification for context-free g…
Static analyzers based on abstract interpretation are complex pieces of software implementing delicate algorithms. Even if static analysis techniques are well understood, their implementation on real languages is still error-prone. This…
The importance of transformations and normal forms in logic programming, and generally in computer science, is well documented. This paper investigates transformations and normal forms in the context of Defeasible Logic, a simple but…
Often, when analyzing the behaviour of systems modelled as context-free languages, we wish to know if two languages overlap. To this end, we present an effective semi-decision procedure for regular separability of context-free languages,…
This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis of the logical models and…
We deal with a normal form for context-free grammars, called Dyck normal form. This normal form is a syntactical restriction of the Chomsky normal form, in which the two nonterminals occurring on the right-hand side of a rule are paired…
We study a formalization of the grammar induction problem that models sentences as being generated by a compound probabilistic context-free grammar. In contrast to traditional formulations which learn a single stochastic grammar, our…
We propose a simple, yet expressive proof representation from which proofs for different proof assistants can easily be generated. The representation uses only a few inference rules and is based on a frag- ment of first-order logic called…
In this paper, we facilitate the reasoning about impure programming languages, by annotating terms with `decorations' that describe what computational (side) effect evaluation of a term may involve. In a point-free categorical…
We phrase parsing with context-free expressions as a type inhabitation problem where values are parse trees and types are context-free expressions. We first show how containment among context-free and regular expressions can be reduced to a…
Autoformalization has emerged as a term referring to the automation of formalization - specifically, the formalization of mathematics using interactive theorem provers (proof assistants). Its rapid development has been driven by progress in…
The concept of context-free grammar in Combinatorics was first introduced by Chen in 1993. In 1996, Dumont significantly extended the theory of context-free grammars to a variety of other combinatorial models. Substantial progress in this…
We study the computational complexity of universality and inclusion problems for unambiguous finite automata and context-free grammars. We observe that several such problems can be reduced to the universality problem for unambiguous…
In this paper, we propose a globally normalized model for context-free grammar (CFG)-based semantic parsing. Instead of predicting a probability, our model predicts a real-valued score at each step and does not suffer from the label bias…
Mathematics formalisation is the task of writing mathematics (i.e., definitions, theorem statements, proofs) in natural language, as found in books and papers, into a formal language that can then be checked for correctness by a program. It…
Algorithms on grammars/transducers with context-free derivations: hypergraph reachability, shortest path, and inside-outside pruning of 'relatively useless' arcs that are unused by any near-shortest paths.
We consider the language consisting of all words such that it is possible to obtain the empty word by iteratively deleting powers. It turns out that in the case of deleting squares in binary words this language is regular, and in the case…
We study the computational complexity of universality and inclusion problems for unambiguous finite automata and context-free grammars. We observe that several such problems can be reduced to the universality problem for unambiguous…
Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…
Large language models (LLMs) show remarkable promise for democratizing automated reasoning by generating formal specifications. However, a fundamental tension exists: LLMs are probabilistic, while formal verification demands deterministic…
Two formalisms, both based on context-free grammars, have recently been proposed as a basis for a non-uniform random generation of combinatorial objects. The former, introduced by Denise et al, associates weights with letters, while the…