8,744 research outputs found
Process Realizability
We develop a notion of realizability for Classical Linear Logic based on a
concurrent process calculus.Comment: Appeared in Foundations of Secure Computation: Proceedings of the
1999 Marktoberdorf Summer School, F. L. Bauer and R. Steinbruggen, eds. (IOS
Press) 2000, 167-18
Realizability Toposes from Specifications
We investigate a framework of Krivine realizability with I/O effects, and
present a method of associating realizability models to specifications on the
I/O behavior of processes, by using adequate interpretations of the central
concepts of `pole' and `proof-like term'. This method does in particular allow
to associate realizability models to computable functions.
Following recent work of Streicher and others we show how these models give
rise to triposes and toposes
Bar recursion in classical realisability : dependent choice and continuum hypothesis
This paper is about the bar recursion operator in the context of classical
realizability. After the pioneering work of Berardi, Bezem & Coquand [1], T.
Streicher has shown [10], by means of their bar recursion operator, that the
realizability models of ZF, obtained from usual models of -calculus
(Scott domains, coherent spaces, . . .), satisfy the axiom of dependent choice.
We give a proof of this result, using the tools of classical realizability.
Moreover, we show that these realizability models satisfy the well ordering of
and the continuum hypothesis These formulas are therefore realized
by closed -terms. This allows to obtain programs from proofs of
arithmetical formulas using all these axioms.Comment: 11 page
Machine-Checked Proofs For Realizability Checking Algorithms
Virtual integration techniques focus on building architectural models of
systems that can be analyzed early in the design cycle to try to lower cost,
reduce risk, and improve quality of complex embedded systems. Given appropriate
architectural descriptions, assume/guarantee contracts, and compositional
reasoning rules, these techniques can be used to prove important safety
properties about the architecture prior to system construction. For these
proofs to be meaningful, each leaf-level component contract must be realizable;
i.e., it is possible to construct a component such that for any input allowed
by the contract assumptions, there is some output value that the component can
produce that satisfies the contract guarantees. We have recently proposed (in
[1]) a contract-based realizability checking algorithm for assume/guarantee
contracts over infinite theories supported by SMT solvers such as linear
integer/real arithmetic and uninterpreted functions. In that work, we used an
SMT solver and an algorithm similar to k-induction to establish the
realizability of a contract, and justified our approach via a hand proof. Given
the central importance of realizability to our virtual integration approach, we
wanted additional confidence that our approach was sound. This paper describes
a complete formalization of the approach in the Coq proof and specification
language. During formalization, we found several small mistakes and missing
assumptions in our reasoning. Although these did not compromise the correctness
of the algorithm used in the checking tools, they point to the value of
machine-checked formalization. In addition, we believe this is the first
machine-checked formalization for a realizability algorithm.Comment: 14 pages, 1 figur
Existential witness extraction in classical realizability and via a negative translation
We show how to extract existential witnesses from classical proofs using
Krivine's classical realizability---where classical proofs are interpreted as
lambda-terms with the call/cc control operator. We first recall the basic
framework of classical realizability (in classical second-order arithmetic) and
show how to extend it with primitive numerals for faster computations. Then we
show how to perform witness extraction in this framework, by discussing several
techniques depending on the shape of the existential formula. In particular, we
show that in the Sigma01-case, Krivine's witness extraction method reduces to
Friedman's through a well-suited negative translation to intuitionistic
second-order arithmetic. Finally we discuss the advantages of using call/cc
rather than a negative translation, especially from the point of view of an
implementation.Comment: 52 pages. Accepted in Logical Methods for Computer Science (LMCS),
201
On the generalization of linear least mean squares estimation to quantum systems with non-commutative outputs
The purpose of this paper is to study the problem of generalizing the
Belavkin-Kalman filter to the case where the classical measurement signal is
replaced by a fully quantum non-commutative output signal. We formulate a least
mean squares estimation problem that involves a non-commutative system as the
filter processing the non-commutative output signal. We solve this estimation
problem within the framework of non-commutative probability. Also, we find the
necessary and sufficient conditions which make these non-commutative estimators
physically realizable. These conditions are restrictive in practice.Comment: 31 page
Interactive Learning-Based Realizability for Heyting Arithmetic with EM1
We apply to the semantics of Arithmetic the idea of ``finite approximation''
used to provide computational interpretations of Herbrand's Theorem, and we
interpret classical proofs as constructive proofs (with constructive rules for
) over a suitable structure \StructureN for the language of
natural numbers and maps of G\"odel's system \SystemT. We introduce a new
Realizability semantics we call ``Interactive learning-based Realizability'',
for Heyting Arithmetic plus \EM_1 (Excluded middle axiom restricted to
formulas). Individuals of \StructureN evolve with time, and
realizers may ``interact'' with them, by influencing their evolution. We build
our semantics over Avigad's fixed point result, but the same semantics may be
defined over different constructive interpretations of classical arithmetic
(Berardi and de' Liguoro use continuations). Our notion of realizability
extends intuitionistic realizability and differs from it only in the atomic
case: we interpret atomic realizers as ``learning agents''
A Local Logic for Realizability in Web Service Choreographies
Web service choreographies specify conditions on observable interactions
among the services. An important question in this regard is realizability:
given a choreography C, does there exist a set of service implementations I
that conform to C ? Further, if C is realizable, is there an algorithm to
construct implementations in I ? We propose a local temporal logic in which
choreographies can be specified, and for specifications in the logic, we solve
the realizability problem by constructing service implementations (when they
exist) as communicating automata. These are nondeterministic finite state
automata with a coupling relation. We also report on an implementation of the
realizability algorithm and discuss experimental results.Comment: In Proceedings WWV 2014, arXiv:1409.229
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