Publications associées à Arithmétique de Presburger

Interpolation and Quantifiers in Ortholattices

Viktor Kuncak, Simon Guilloud, Sankalp Gambhir

We study quantifiers and interpolation properties in ortho- logic, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We present a sequent-based p ...

2024

Interpolation and Quantifiers in Ortholattices

Viktor Kuncak, Simon Guilloud, Sankalp Gambhir

We study quantifiers and interpolation properties in orthologic, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We present a sequent-based pro ...

Springer International Publishing Ag2024

Energy Efficient Logic and Memory Design With Beyond-CMOS Magnetoelectric Spin-Orbit (MESO) Technology Toward Ultralow Supply Voltage

Kyojin Choo

Devices based on the spin as the fundamental computing unit provide a promising beyond-complementary metal-oxide-semiconductor (CMOS) device option, thanks to their energy efficiency and compatibility with CMOS. One such option is a magnetoelectric spin-or ...

Ieee-Inst Electrical Electronics Engineers Inc2023

Decision Procedures for Power Structures

Rodrigo Raya

We study the decision problem for the existential fragment of the theory of power structures. We prove complexity results that parallel the decidability results of Feferman-Vaught for the theories of product structures thereby showing that the construction ...

EPFL2023

Leibniz en Créateur. Un regard matériel sur sa machine à calculer

Simon François Dumas Primbault

Between 1671 and 1716, the German mathematician Gottfried Wilhelm Leibniz attempted to design a reckoning machine. Working closely with the Parisian clockmaker Monsieur Ollivier, Leibniz eventually failed at producing a working prototype. After the redisco ...

2022

Computing Cyclic Isogenies between Principally Polarized Abelian Varieties over Finite Fields

Marius Lorenz Vuille

Abelian varieties are fascinating objects, combining the fields of geometry and arithmetic. While the interest in abelian varieties has long time been of purely theoretic nature, they saw their first real-world application in cryptography in the mid 1980's ...

EPFL2020

Nonlinear evolution of the centrifugal instability using a semilinear model

François Gallaire, Eunok Yim

We study the nonlinear evolution of the axisymmetric centrifugal instability developing on a columnar anticyclone with a Gaussian angular velocity using a semilinear approach. The model consists of two coupled equations: one for the linear evolution of the ...

Cambridge University Press2020

Solving quantified linear arithmetic by counterexample-guided instantiation

Viktor Kuncak, Andrew Joseph Reynolds

This paper presents a framework to derive instantiation-based decision procedures for satisfiability of quantified formulas in first-order theories, including its correctness, implementation, and evaluation. Using this framework we derive decision procedur ...

2017

Improving Circuit Mapping Performance Through MIG-based Synthesis for Carry Chains

Giovanni De Micheli, Paolo Ienne, Mathias Soeken, Grace Zgheib, Xifan Tang, Pierre-Emmanuel Julien Marc Gaillardon, Ana Petkovska, Luca Gaetano Amarù, Zhufei Chu

Hard-wired carry chains in FPGAs are designed to improve efficiency of important arithmetic primitives. Although they are proven to be effective for arithmetic-rich functions, there are very few studies on the optimization opportunities of carry chains for ...

ACM2017

Method and apparatus for low complexity spectral analysis of bio-signals

David Atienza Alonso, Andreas Peter Burg, Srinivasan Murali, Georgios Karakonstantis, Aviinaash Sankaranarayanan

A method and device for reducing the computational complexity of a processing algorithm, of a discrete signal, in particular of the spectral estimation and analysis of bio-signals, with minimum or no quality loss, which comprises steps of (a) choosing a do ...

2015

A Decision Procedure for Regular Membership and Length Constraints over Unbounded Strings

Andrew Joseph Reynolds

We prove that the quantifier-free fragment of the theory of character strings with regular language membership constraints and linear integer constraints over string lengths is decidable. We do that by describing a sound, complete and terminating tableaux ...

Springer-Verlag Berlin2015

Generalized Bombieri-Lagarias' Theorem And Generalized Li'S Criterion With Its Arithmetic Interpretation

Serguei Sekatski

We show that Li's criterion equivalent to the Riemann hypothesis, i.e., the statement that the sums k(n) = Sigma(rho)(1-(1-1/rho)(n)) over zeros of the Riemann xi-function and the derivatives lambda(n) equivalent to 1/(n-1)! d(n)/dz(n)(z(n-1) ln (xi(z)))ve ...

Springer Verlag2014

A Verification Toolkit for Numerical Transition Systems

Viktor Kuncak, Hossein Hojjat

This paper presents a publicly available toolkit and a benchmark suite for rigorous verification of Integer Numerical Transition Systems (INTS), which can be viewed as control-flow graphs whose edges are annotated by Presburger arithmetic formulas. We pres ...

2012

Software Synthesis Procedures

Viktor Kuncak, Mikaël Mayer, Philippe Paul Henri Suter, Ruzica Piskac

Automated synthesis of program fragments from specifications can make programs easier to write and easier to reason about. To integrate synthesis into programming languages, software synthesis algorithms should behave in a predictable way: they should succ ...

2012

A lattice in more than two Kac–Moody groups is arithmetic

Nicolas Monod

Let Gamma be an irreducible lattice in a product of n infinite irreducible complete Kac–Moody groups of simply laced type over finite fields. We show that if n>2, then each Kac–Moody groups is in fact a simple algebraic group over a local field and Gamma i ...

2012

Sets with Cardinality Constraints in Satisfiability Modulo Theories

Viktor Kuncak, Philippe Paul Henri Suter, Robin Steiger

Boolean Algebra with Presburger Arithmetic (BAPA) is a decidable logic that can express constraints on sets of elements and their cardinalities. Problems from verification of complex properties of software often contain fragments that belong to quantifier- ...

Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2011

Decision Procedures for Program Synthesis and Verification

Ruzica Piskac

Decision procedures are widely used in software development and verification. The goal of this dissertation is to increase the scope of properties that can be verified using decision procedures. To achieve this goal, we identify three improvements over the ...

EPFL2011

Ordered Sets in the Calculus of Data Structures

Viktor Kuncak, Philippe Paul Henri Suter, Ruzica Piskac

Our goal is to identify families of relations that are useful for reasoning about software. We describe such families using decidable quantifier-free classes of logical constraints with a rich set of operations. A key challenge is to define such classes of ...

Springer2010

Building a Calculus of Data Structures

Viktor Kuncak, Philippe Paul Henri Suter, Ruzica Piskac

Techniques such as verification condition generation, predicate abstraction, and expressive type systems reduce software verification to proving formulas in expressive logics. Programs and their specifications often make use of data structures such as sets ...

Springer2010

Combining Theories with Shared Set Operations

Viktor Kuncak, Ruzica Piskac

Motivated by applications in software verification, we explore automated reasoning about the non-disjoint combination of theories of infinitely many finite structures, where the theories share set variables and set operations. We prove a combination theore ...

Springer2009