Related papers: A Classical Realizability Model arising from a Sta…
We give an explicit construction of irreducible modules over Khovanov-Lauda-Rouquier algebras $R$ and their cyclotomic quotients $R^{\lambda}$ for finite classical types using a crystal basis theoretic approach. More precisely, for each…
Classical evaluations of configurations of intertwined quantum contexts induce relations, such as true-implies-false, true-implies-true, but also nonseparability among the input and output terminals. When combined, these exploitable…
We introduce a simple extension of the $\lambda$-calculus with pairs---called the distributive $\lambda$-calculus---obtained by adding a computational interpretation of the valid distributivity isomorphism $A \Rightarrow (B\wedge C)\ \…
We consider different classes of combinatory structures related to Krivine realizability. We show, in the precise sense that they give rise to the same class of triposes, that they are equivalent for the purpose of modeling higher-order…
We revisit a fundamental result in real-time verification, namely that the binary reachability relation between configurations of a given timed automaton is definable in linear arithmetic over the integers and reals. In this paper we give a…
The extensive deployment of probabilistic algorithms has radically changed our perspective on several well-established computational notions. Correctness is probably the most basic one. While a typical probabilistic program cannot be said…
In this paper we introduce a typed, concurrent $\lambda$-calculus with references featuring explicit substitutions for variables and references. Alongside usual safety properties, we recover strong normalization. The proof is based on a…
The method of using concepts and insight from quantum information theory in order to solve problems in reversible classical computing (introduced in Ref. [1]) have been generalized to irreversible classical computing. The method have been…
By combining well-known techniques from both noncommutative algebra and computational commutative algebra, we observe that an algorithmic approach can be applied to the study of irreducible representations of finitely presented algebras. In…
We show how to transform into programs the proofs in classical Analysis which use the existence of an ultrafilter on the integers. The method mixes the classical realizability introduced by the author, with the "forcing" of P. Cohen. The…
In recent years, there has been increasing interest in explanation methods for neural model predictions that offer precise formal guarantees. These include abductive (respectively, contrastive) methods, which aim to compute minimal subsets…
Programs with control are usually modeled using lambda calculus extended with control operators. Instead of modifying lambda calculus, we consider a different model of computation. We introduce continuation calculus, or CC, a deterministic…
Classical circuit complexity characterizes parallel computation in purely combinatorial terms, ignoring the physical constraints that govern real hardware. The standard classes $\mathbf{NC}$, $\mathbf{AC}$, and $\mathbf{TC}$ treat unlimited…
A longstanding open problem is whether there exists a non-syntactical model of untyped lambda-calculus whose theory is exactly the least equational lambda-theory (=Lb). In this paper we make use of the Visser topology for investigating the…
A class of models is presented, in the form of continuation monads polymorphic for first-order individuals, that is sound and complete for minimal intuitionistic predicate logic. The proofs of soundness and completeness are constructive and…
We study an expressive model of timed pushdown automata extended with modular and fractional clock constraints. We show that the binary reachability relation is effectively expressible in hybrid linear arithmetic with a rational and an…
It is discussed a practical possibility of a provable programming of mathematics basing on intuitionism and the dependent types feature of a programming language.The principles of constructive mathematics and provable programming are…
We prove the undecidability of the third order pattern matching problem in typed lambda-calculi with dependent types and in those with type constructors by reducing the second order unification problem to them.
The present paper introduces a novel notion of `(effective) computability', called viability, of strategies in game semantics in an intrinsic (i.e., without recourse to the standard Church-Turing computability), non-inductive and…
Cubical type theory is an extension of Martin-L\"of type theory recently proposed by Cohen, Coquand, M\"ortberg and the author which allows for direct manipulation of $n$-dimensional cubes and where Voevodsky's Univalence Axiom is provable.…