Related papers: Tuple Interpretations for Higher-Order Rewriting
Tuple interpretations are a class of algebraic interpretation that subsumes both polynomial and matrix interpretations as it does not impose simple termination and allows non-linear interpretations. It was developed in the context of…
Time complexity in rewriting is naturally understood as the number of steps needed to reduce terms to normal forms. Establishing complexity bounds to this measure is a well-known problem in the rewriting community. A vast majority of…
In this short paper, we consider a form of higher-order rewriting with a call-by-value evaluation strategy so as to model call-by-value programs. We briefly present a cost-size semantics to call-by-value rewriting: a class of algebraic…
Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…
The class of type-two basic feasible functionals ($\mathtt{BFF}_2$) is the analogue of $\mathtt{FP}$ (polynomial time functions) for type-2 functionals, that is, functionals that can take (first-order) functions as arguments.…
All current investigations to analyze the derivational complexity of term rewrite systems are based on a single termination method, possibly preceded by transformations. However, the exclusive use of direct criteria is problematic due to…
The termination method of weakly monotonic algebras, which has been defined for higher-order rewriting in the HRS formalism, offers a lot of power, but has seen little use in recent years. We adapt and extend this method to the alternative…
We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques…
We introduce an operational rewriting-based semantics for strictly positive nested higher-order (co)inductive types. The semantics takes into account the "limits" of infinite reduction sequences. This may be seen as a refinement and…
Constructor rewriting systems are said to be cons-free if any constructor term occurring in the rhs of a rule must be a subterm of the lhs of the rule. Roughly, such systems cannot build new data structures during their evaluation. In…
We propose a notion of complexity for oriented conditional term rewrite systems satisfying certain restrictions. This notion is realistic in the sense that it measures not only successful computations, but also partial computations that…
Several types of term rewriting systems can be distinguished by the way their rules overlap. In particular, we define the classes of prefix, suffix, bottom-up and top-down systems, which generalize similar classes on words. Our aim is to…
We introduce a novel resource analysis for typed term rewrite systems based on a potential-based type system. This type system gives rise to polynomial bounds on the innermost runtime complexity. We relate the thus obtained amortised…
We show how the complexity of higher-order functional programs can be analysed automatically by applying program transformations to a defunctionalized versions of them, and feeding the result to existing tools for the complexity analysis of…
We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques…
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…
With the Generative Pre-trained Transformer 3.5 (GPT-3.5) exhibiting remarkable reasoning and comprehension abilities in Natural Language Processing (NLP), most Question Answering (QA) research has primarily centered around general QA tasks…
Higher-dimensional rewriting systems are tools to analyse the structure of formally reducing terms to normal forms, as well as comparing the different reduction paths that lead to those normal forms. This higher structure can be captured by…
In this paper we examine a number of term rewriting system for integer number representations, building further upon the datatype defining systems described in [2]. In particular, we look at automated methods for proving confluence and…
Current representations used in reasoning steps of large language models can mostly be categorized into two main types: (1) natural language, which is difficult to verify; and (2) non-natural language, usually programming code, which is…