Related papers: Modular Complexity Analysis for Term Rewriting

Compositional generalization refers to correctly interpret novel combinations of known primitives, which remains a major challenge. Existing approaches often rely on supervised fine-tuning, which encourages models to imitate target outputs.…

We establish new, and surprisingly tight, connections between propositional proof complexity and finite model theory. Specifically, we show that the power of several propositional proof systems, such as Horn resolution, bounded-width…

A high degree of topical diversity is often considered to be an important characteristic of interesting text documents. A recent proposal for measuring topical diversity identifies three elements for assessing diversity: words, topics, and…

Rewriting is a framework for reasoning about functional programming. The dependency pair criterion is a well-known mechanism to analyze termination of term rewriting systems. Functional specifications with an operational semantics based on…

Logically constrained term rewrite systems (LCTRSs) are a rewriting formalism that naturally supports built-in data structures, including integers and bit-vectors. The recent framework of existentially constrained terms and most general…

Higher-order rewriting is a framework in which one can write higher-order programs and study their properties. One such property is termination: the situation that for all inputs, the program eventually halts its execution and produces an…

In deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems---such as for instance natural deduction---are applied. Therefore, the…

Narrowing is a procedure that was first studied in the context of equational E-unification and that has been used in a wide range of applications. The classic completeness result due to Hullot states that any term rewriting derivation…

Logically constrained term rewriting is a relatively new rewriting formalism that naturally supports built-in data structures, such as integers and bit vectors. In the analysis of logically constrained term rewrite systems (LCTRSs),…

In this paper, we survey the complexity of distinct methods that allow the programmer to synthesize a sup-interpretation, a function providing an upper- bound on the size of the output values computed by a program. It consists in a static…

The matrices and their sub-blocks are introduced into the study of determining various extensions in the sense of Dung's theory of argumentation frameworks. It is showed that each argumentation framework has its matrix representations, and…

Rewriting techniques based on reduction orderings generate "just enough" consequences to retain first-order completeness. This is ideal for superposition-based first-order theorem proving, but for at least one approach to inductive…

This paper proposes a theoretical framework which models the information provided by retrieval systems in terms of Information Theory. The proposed framework allows to formalize: (i) system effectiveness as an information theoretic…

Being able to interpret, or explain, the predictions made by a machine learning model is of fundamental importance. This is especially true when there is interest in deploying data-driven models to make high-stakes decisions, e.g. in…

Counting distinct permutations with replacement, especially when involving multiple subwords, is a longstanding challenge in combinatorial analysis, with critical applications in cryptography, bioinformatics, and statistical modeling. This…

For the whole class of linear term rewriting systems, we define \emph{bottom-up rewriting} which is a restriction of the usual notion of rewriting. We show that bottom-up rewriting effectively inverse-preserves recognizability and analyze…

A rewriting system is a set of equations over a given set of terms called rules that characterize a system of computation and is a powerful general method for providing decision procedures of equational theories, based upon the principle of…

Term graph rewriting provides a formalism for implementing term rewriting in an efficient manner by avoiding duplication. Infinitary term rewriting has been introduced to study infinite term reduction sequences. Such infinite reductions can…

We propose a modal logic tailored to describe graph transformations and discuss some of its properties. We focus on a particular class of graphs called termgraphs. They are first-order terms augmented with sharing and cycles. Termgraphs…

Rewriting Induction (RI) is a formal system in term rewriting to establish program equivalence. The recently defined Bounded RI for higher-order Logically Constrained Term Rewriting Systems (LCSTRSs) yields a convenient proof system for…