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Non-linear reasoning for invariant synthesis

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Secure Information Flow as a Safety Problem

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Generation of Basic Semi-algebraic Invariants Using Convex Polyhedra

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How to Compose Presburger-Accelerations: Applications to Broadcast Protocols

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Symbolic verification with periodic sets

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Resource Analysis of Complex Programs with Cost Equations

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Ideals, Varieties, and Algorithms

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The SeaHorn Verification Framework

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Polynomial Invariants by Linear Algebra

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Symbolic Implementation of the Best Transformer

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Approximating the Algebraic Relational Semantics of Imperative Programs

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Abstract Interpretation with Alien Expressions and Heap Structures

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Automatic Inference of Upper Bounds for Recurrence Relations in Cost Analysis

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A Numerical Abstract Domain Based on Expression Abstraction and Max Operator with Application in Timing Analysis

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Reasoning Algebraically About P-Solvable Loops

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Z3: An Efficient SMT Solver

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Fast Acceleration of Ultimately Periodic Relations

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ABC: Algebraic Bound Computation for Loops

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Relational Verification Using Product Programs

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CPAchecker: A Tool for Configurable Software Verification

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Ultimate Automizer with SMTInterpol

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Alternating Runtime and Size Complexity Analysis of Integer Programs

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Automating Abstract Interpretation

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An Abstract Domain of Uninterpreted Functions

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The Concrete Tetrahedron

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Introduction to the Operational Calculus

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A Modular Static Analysis Approach to Affine Loop Invariants Detection

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Analytic Combinatorics

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Secure information flow by self-composition

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Compositional recurrence analysis

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Automatic Generation of Polynomial Loop Invariants

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A theoretical basis for the reduction of polynomials to canonical forms

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Newtonian program analysis

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The concrete tetrahedron

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On the Inference of Resource Usage Upper and Lower Bounds

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Inductive invariant generation via abductive inference

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Abstract acceleration of general linear loops

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Abstract acceleration of general linear loops

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Newtonian program analysis via tensor product

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Complexity verification using guided theorem enumeration

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Compositional recurrence analysis revisited

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Decomposition instead of self-composition for proving the absence of timing channels

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Automated Generation of Non-Linear Loop Invariants Utilizing Hypergeometric Sequences

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Automatic discovery of linear restraints among variables of a program

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Systematic design of program analysis frameworks

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Automatic recognition of induction variables and recurrence relations by abstract interpretation

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Non-linear loop invariant generation using Gröbner bases

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Precise interprocedural analysis through linear algebra

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Computer Algebra and Symbolic Computation

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- Analytic combinatorics

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PURRS: Towards Computer Algebra Support for Fully Automatic Worst-Case Complexity Analysis

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Termination of Polynomial Loops

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Counterexample- and Simulation-Guided Floating-Point Loop Invariant Synthesis

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Algebraic Program Analysis

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Synthesis with Asymptotic Resource Bounds

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Reflections on Termination of Linear Loops

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Selectively-Amortized Resource Bounding

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Affine Loop Invariant Generation via Matrix Algebra

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Solving Invariant Generation for Unsolvable Loops

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MDPs as Distribution Transformers: Affine Invariant Synthesis for Safety Objectives

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Automated Sensitivity Analysis for Probabilistic Loops

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Sound and Complete Witnesses for Template-Based Verification of LTL Properties on Polynomial Programs

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Polar: An Algebraic Analyzer for (Probabilistic) Loops

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Array-Carrying Symbolic Execution for Function Contract Generation

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Invariant Generation for Multi-Path Loops with Polynomial Assignments

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Numerical Invariants via Abstract Machines

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Constraint Based Invariant Generation with Modular Operations

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Invariant relations for affine loops

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Abstractions of sequences, functions and operators

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(Un)Solvable loop analysis

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A novel data-driven approach on inferring loop invariants for C programs

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First order Büchi automata and their application to verification of LTL specifications

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Modular Invariant Generation via Constraint Solving

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Denotational semantics as a foundation for cost recurrence extraction for functional languages

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A Machine Learning-Based Approach for Solving Recurrence Relations and Its use in Cost Analysis of Logic Programs

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Demystifying Template-Based Invariant Generation for Bit-Vector Programs

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Requirement-Dependent Extra Invariant Patterns in Deductive Verification of PoST Programs

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Property Oriented Verification Via Iterative Abstract Interpretation

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Automatic Amortized Resource Analysis with Regular Recursive Types

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A Novel Data-Driven Approach for Generating Verified Loop Invariants

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Polynomial Invariants for Affine Programs

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Closed forms for numerical loops

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Recurrence extraction for functional programs through call-by-push-value

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Selectively-Amortized Resource Bounding (Extended Version)

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