Related papers: On Complexity Bounds and Confluence of Parallel Te…
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…
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…
There are many evaluation strategies for term rewrite systems, but automatically proving termination or analyzing complexity is usually easiest for innermost rewriting. Several syntactic criteria exist when innermost termination implies…
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…
Logically constrained rewrite systems (LCTRSs) are a versatile and efficient rewriting formalism that can be used to model programs from various programming paradigms, as well as simplification systems in compilers and SMT solvers. In this…
Recently, many techniques have been introduced that allow the (automated) classification of the runtime complexity of term rewrite systems (TRSs for short). In earlier work, the authors have shown that for confluent TRSs, innermost…
We present a technique to infer lower bounds on the worst-case runtime complexity of integer programs, where in contrast to earlier work, our approach is not restricted to tail-recursion. Our technique constructs symbolic representations of…
We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating…
We develop a class of algebraic interpretations for many-sorted and higher-order term rewriting systems that takes type information into account. Specifically, base-type terms are mapped to \emph{tuples} of natural numbers and higher-order…
In earlier work, we developed an approach for automatic complexity analysis of integer programs, based on an alternating modular inference of upper runtime and size bounds for program parts. In this paper, we show how recent techniques to…
We present a way to implement term rewriting on a GPU. We do this by letting the GPU repeatedly perform a massively parallel evaluation of all subterms. We find that if the term rewrite systems exhibit sufficient internal parallelism, GPU…
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…
We study the problem of parametric parallel complexity analysis of concurrent, message-passing programs. To make the analysis local and compositional, it is based on a conservative extension of binary session types, which structure the type…
Term rewriting plays a crucial role in software verification and compiler optimization. With dozens of highly parameterizable techniques developed to prove various system properties, automatic term rewriting tools work in an extensive…
Parallel fixed-parameter tractability studies how parameterized problems can be solved in parallel. A surprisingly large number of parameterized problems admit a high level of parallelization, but this does not mean that we can also…
This paper presents a new abstract method for proving lower bounds in computational complexity. Based on the notion of topological and measurable entropy for dynamical systems, it is shown to generalise three previous lower bounds results…
With the increasing capabilities of Large Language Models (LLMs), parallel reasoning has emerged as a new inference paradigm that enhances reasoning robustness by concurrently exploring multiple lines of thought before converging on a final…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
Supercomputers are equipped with an increasingly large number of cores to use computational power as a way of solving problems that are otherwise intractable. Unfortunately, getting serial algorithms to run in parallel to take advantage of…
Recent advances in large language models (LLMs) have accelerated progress toward artificial general intelligence, with inference-time scaling emerging as a key technique. Contemporary approaches leverage either sequential reasoning…