Related papers: Computing with Infinite Objects: the Gray Code Cas…
Models of computation operating over the real numbers and computing a larger class of functions compared to the class of general recursive functions invariably introduce a non-finite element of infinite information encoded in an arbitrary…
We introduce an infinitary first order linear logic with least and greatest fixed points. To ensure cut elimination, we impose a validity condition on infinite derivations. Our calculus is designed to reason about rich signatures of…
e use Prolog as a flexible meta-language to provide executable specifications of some fundamental mathematical objects and their transformations. In the process, isomorphisms are unraveled between natural numbers and combinatorial objects…
Formal verification using the model checking paradigm has to deal with two aspects: The system models are structured, often as products of components, and the specification logic has to be expressive enough to allow the formalization of…
Nakano's later modality can be used to specify and define recursive functions which are causal or synchronous; in concert with a notion of clock variable, it is possible to also capture the broader class of productive (co)programs. Until…
We give the first two algorithms to enumerate all binary words of $\{0,1\}^\ell$ (like Gray codes) while ensuring that the delay and the auxiliary space is independent from $\ell$, i.e., constant time for each word, and constant memory in…
In type theory, coinductive types are used to represent processes, and are thus crucial for the formal verification of non-terminating reactive programs in proof assistants based on type theory, such as Coq and Agda. Currently, programming…
The topological interpretation of modal logics provides descriptive languages and proof systems for reasoning about points of topological spaces. Recent work has been devoted to model checking of spatial logics on discrete spatial…
In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…
This article contains a proposal to add coinduction to the computational apparatus of natural language understanding. This, we argue, will provide a basis for more realistic, computationally sound, and scalable models of natural language…
This work explores an unexpected application of Implicit Computational Complexity (ICC) to parallelize loops in imperative programs. Thanks to a lightweight dependency analysis, our algorithm allows splitting a loop into multiple loops that…
Analog computation is an alternative to digital computation, that has recently re-gained prominence, since it includes neural networks and neuromorphic computing. Further important examples are cellular automata and differential analyzers.…
We develop synthetic notions of oracle computability and Turing reducibility in the Calculus of Inductive Constructions (CIC), the constructive type theory underlying the Coq proof assistant. As usual in synthetic approaches, we employ a…
This paper discusses limitations of reflexive and diagonal arguments as methods of proof of limitative theorems (e.g. G\"odel's theorem on Entscheidungsproblem, Turing's halting problem or Chaitin-G\"odel's theorem). The fact, that a formal…
Neither the classical nor intuitionistic logic traditions are perfectly-aligned with the purpose of reasoning about computation, in that neither tradition can permit unconstrained recursive definitions without inconsistency: recursive…
Earlier, the authors introduced the logic IntGC, which is an extension of intuitionistic propositional logic by two rules of inference mimicking the performance of Galois connections (Logic J. of the IGPL, 18:837-858, 2010). In this paper,…
We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already,…
The goal of group testing is to efficiently identify a few specific items, called positives, in a large population of items via tests. A test is an action on a subset of items which returns positive if the subset contains at least one…
We devise a variable precision floating-point arithmetic by exploiting the framework provided by the Infinity Computer. This is a computational platform implementing the Infinity Arithmetic system, a positional numeral system which can…
Whereas an extension with non-interference of Hoare logic for sequential programs Owicki--Gries logic ensures the correctness of concurrent programs on strict consistency, it is unsound to weak memory models adopted by modern computer…