Related papers: Process Realizability
This paper shows that the basic logic induced by the parallel recurrence of Computability Logic is a proper superset of the basic logic induced by the branching recurrence. The latter is known to be precisely captured by the cirquent…
We study counting propositional logic as an extension of propositional logic with counting quantifiers. We prove that the complexity of the underlying decision problem perfectly matches the appropriate level of Wagner's counting hierarchy,…
We extend the signal flow calculus---a compositional account of the classical signal flow graph model of computation---to encompass affine behaviour, and furnish it with a novel operational semantics. The increased expressive power allows…
We construct a family of processes, from a renewal process, that have realizations that converge almost surely to the Brownian motion, uniformly on the unit time interval. Finally we compute the rate of convergence in a particular case.
We present a unifying framework for type systems for process calculi. The core of the system provides an accurate correspondence between essentially functional processes and linear logic proofs; fragments of this system correspond to…
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…
Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…
Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the top-level logical symbol of that formula. We…
We develop a classical propositional logic for reasoning about combinatory logic. We define its syntax, axiomatic system and semantics. The syntax and axiomatic system are presented based on classical propositional logic, with typed…
For formulas of the Implicational Propositional Calculus (IPC) that are theorems of the classical Propositional Calculus (PC) we show that PC proofs yield IPC proofs. As a consequence, completeness of PC yields completeness of IPC.
A $\lambda$-calculus is introduced in which all programs can be evaluated in probabilistic polynomial time and in which there is sufficient structure to represent sequential cryptographic constructions and adversaries for them, even when…
We develop a notion of computability and complexity of functions over the reals, which seems to be very natural when one tries to determine just how "difficult" a certain function is. This notion can be viewed as an extension of both BSS…
This paper considers the problem of maximizing multiple linear functions over the probability simplex. A classification of feasible points is indicated. A necessary and sufficient condition for a member of each class to be an efficient…
Linearizability is the commonly accepted notion of correctness for concurrent data structures. It requires that any execution of the data structure is justified by a linearization --- a linear order on operations satisfying the data…
The case for the International Linear Collider and the prospects for its realisation as well as possible timelines are discussed.
In this paper we extend the predicate logic introduced in [Beauquier et al. 2002] in order to deal with Semi-Markov Processes. We prove that with respect to qualitative probabilistic properties, model checking is decidable for this logic…
We develop a theory of modulus triples, for future motivic applications.
Formal reasoning about distributed algorithms (like Consensus) typically requires to analyze global states in a traditional state-based style. This is in contrast to the traditional action-based reasoning of process calculi. Nevertheless,…
We introduce the notion of implicative algebra, a simple algebraic structure intended to factorize the model constructions underlying forcing and realizability (both in intuitionistic and classical logic). The salient feature of this…
Recently, in order to mix algebraic and logic styles of specification in a uniform framework, the notion of a logic labelled transition system (Logic LTS or LLTS for short) has been introduced and explored. A variety of constructors over…