Related papers: Complexity Bounds for Ordinal-Based Termination

In a previous work, the first author extended to higher-order rewriting and dependent types the use of size annotations in types, a termination proof technique called type or size based termination and initially developed for ML-like…

We study the complexity of automatic structures via well-established concepts from both logic and model theory, including ordinal heights (of well-founded relations), Scott ranks of structures, and Cantor-Bendixson ranks (of trees). We…

This thesis is concerned with investigations into the "complexity of term rewriting systems". Moreover the majority of the presented work deals with the "automation" of such a complexity analysis. The aim of this introduction is to present…

We prove level-by-level upper and lower bounds on the strength of determinacy for finite differences of sets in the hyperarithmetical hierarchy in terms of subsystems of finite-and transfinite-order arithmetic, extending the…

We present a simple new method for proving that languages are not regular. We prove the correctness of the method, illustrate the ease of using the method on well-known examples of nonregular languages, and prove two additional theorems on…

This talk is a sneak preview of the project, 'proof theory for theories of ordinals'. Background, aims, survey and furture works on the project are given. Subsystems of second order arithmetic are embedded in recursively large ordinals and…

One method to determine whether or not a system of partial differential equations is consistent is to attempt to construct a solution using merely the "algebraic data" associated to the system. In technical terms, this translates to the…

A model of computation for which reasonable yet still incomplete lower bounds are known is the read-once branching program. Here variants of complexity measures successful in the study of read-once branching programs are defined and…

In this paper we study a very general finite Ramsey theorem, where both the sets being colored and the homogeneous set must satisfy some largeness notion. For the homogeneous set this has already been done using the notion of…

Proving program termination is key to guaranteeing absence of undesirable behaviour, such as hanging programs and even security vulnerabilities such as denial-of-service attacks. To make termination checks scale to large systems,…

We introduce a method for proving almost sure termination in the context of lambda calculus with continuous random sampling and explicit recursion, based on ranking supermartingales. This result is extended in three ways. Antitone ranking…

We consider the termination/non-termination property of a class of loops. Such loops are commonly used abstractions of real program pieces. Second-order logic is a convenient language to express non-termination. Of course, such property is…

Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…

Program correctness (in imperative and functional programming) splits in logic programming into correctness and completeness. Completeness means that a program produces all the answers required by its specification. Little work has been…

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…

We investigate the complexity of the satisfiability problem for a modal logic expressing `knowing how' assertions, related to an agent's abilities to achieve a certain goal. We take one of the most standard semantics for this kind of logics…

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…

We present a new algorithm for computing upper bounds on the number of executions of each program instruction during any single program run. The upper bounds are expressed as functions of program input values. The algorithm is primarily…

Predicting the runtime complexity of a programming code is an arduous task. In fact, even for humans, it requires a subtle analysis and comprehensive knowledge of algorithms to predict time complexity with high fidelity, given any code. As…

Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…