Concept

Theory (mathematical logic)

Related publications (22)

LISA – A Modern Proof System

Viktor Kuncak, Simon Guilloud, Sankalp Gambhir

We present LISA, a proof system and proof assistant for constructing proofs in schematic first-order logic and axiomatic set theory. The logical kernel of the system is a proof checker for first-order logic with equality and schematic predicate and fun ...

2023

On Polynomial Algorithms for Normalizing Formulas

Viktor Kuncak, Simon Guilloud, Mario Bucev

We propose a new approach for normalization and simplification of logical formulas. Our approach is based on algorithms for lattice-like structures. Specifically, we present two efficient algorithms for computing a normal form and deciding the word problem ...

2022

Equivalence Checking for Orthocomplemented Bisemilattices in Log-Linear Time

Viktor Kuncak, Simon Guilloud

We present a quasilinear time algorithm to decide the word problem on a natural algebraic structures we call orthocomplemented bisemilattices, a subtheory of boolean algebra. We use as a base a variation of Hopcroft, Ullman and Aho algorithm for tree isomo ...

Springer2022

Scaling Language Features for Program Verification

Georg Stefan Schmid

Formal verification of real-world software systems remains challenging for a number of reasons, including lack of automation, friction in specifying properties, and limited support for the diverse programming paradigms used in industry. In this thesis we m ...

EPFL2022

Mapping and Analysis of the Complexity of Lipid Metabolism for Applications in Health and Sustainability

Vassily Hatzimanikatis, Sofia Tsouka

Metabolism is a network of biotransformations that sustain life in cells. Over the past decades, metabolism has been studied in multiple contexts, ranging from medicine to industrial manufacturing. In particular, lipid metabolism has been linked to various ...

EPFL2020

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

Verification by Reduction to Functional Programs

Régis William Blanc

In this thesis, we explore techniques for the development and verification of programs in a high-level, expressive, and safe programming language. Our programs can express problems over unbounded domains and over recursive and mutable data structures. We p ...

EPFL2017

On Satisfiability for Quantified Formulas in Instantiation-Based Procedures

Viktor Kuncak, Nicolas Charles Yves Voirol

Procedures for first-order logic with equality are used in many modern theorem provers and solvers, yet procedure termination in case of interesting sub-classes of satisfiable formulas remains a challenging problem. We present an instantiation-based semi-d ...

2016

Automating Verification of Functional Programs with Quantified Invariants

Viktor Kuncak, Nicolas Charles Yves Voirol

We present the foundations of a verifier for higher-order functional programs with generics and recursive algebraic data types. Our ver- ifier supports finding sound proofs and counterexamples even in the presence of certain quantified invariants and recur ...

2016

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

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