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Non-linear reasoning for invariant synthesis

Zachary Kincaid, John Cyphert, Jason Breck, Thomas Reps
2017 Proceedings of the ACM on Programming Languages  
For instance, reasoning about exponentials provides a way to find invariants of digital-filter programs, and reasoning about polynomials and/or logarithms is needed for establishing invariants that describe  ...  This paper presents a method for generating non-linear invariants of general loops based on analyzing recurrence relations.  ...  Rybalchenko for their comments on the submission.  ... 
doi:10.1145/3158142 dblp:journals/pacmpl/KincaidCBR18 fatcat:rzj7q45oi5aihjxhduy7e6suqu

Algebra-Based Synthesis of Loops and Their Invariants (Invited Paper) [chapter]

Andreas Humenberger, Laura Kovács
2021 Lecture Notes in Computer Science  
We first describe an algorithmic approach for synthesising all polynomial equality invariants of such non-deterministic numeric single-path loops.  ...  By reverse engineering invariant synthesis, we then describe an automated method for synthesising program loops satisfying a given set of polynomial loop invariants.  ...  We thank Maximillian Jaroschek (TU Wien) for joint work allowing to extend our invariant generation approaches to more complex loops and number sequences.  ... 
doi:10.1007/978-3-030-67067-2_2 fatcat:mzjf6jjlgndu3ehhiwv4v4w7oi

Schema-Guided Synthesis of Imperative Programs by Constraint Solving [chapter]

Michael A. Colón
2005 Lecture Notes in Computer Science  
We present a method for schema-guided synthesis of imperative programs computing polynomial functions and their inverses.  ...  Although non-linear constraint solving is NP-hard, a solution can be generated automatically when the resulting system contains few constraints.  ...  For this reason, tools for automatic constructive synthesis wisely limit themselves to generating loop-free programs [23] .  ... 
doi:10.1007/11506676_11 fatcat:v5g3mlrhxffmrmpv23gtdbew5a

Preliminary Notes on Termination and Non-Termination Reasoning [article]

Ton Chanh Le
2013 arXiv   pre-print
In this preliminary note, we will illustrate our ideas on automated mechanisms for termination and non-termination reasoning.  ...  terminates but a linear ranking function does not exist or (ii) a supporting invariant for termination proving is missing.  ...  Consequently, there is not a linear ranking function for that loop and/or a supporting invariant, which helps to separate terminating and non-terminating execution of the loop, is missing for termination  ... 
arXiv:1309.3128v1 fatcat:2z26ygbs3zghxkn77opyxrceme

Synthesis for Polynomial Lasso Programs [article]

Jan Leike, Ashish Tiwari
2013 arXiv   pre-print
We present a method for the synthesis of polynomial lasso programs.  ...  Central to this approach is the discovery of non-linear (algebraic) loop invariants. We extend Sankaranarayanan, Sipma, and Manna's template-based approach and prove a completeness criterion.  ...  Acknowledgements We would like to thank the anonymous reviewers for their valuable feedback.  ... 
arXiv:1311.4046v1 fatcat:t3o2mz4az5gmrj2zwb2ejihnh4

Synthesis for Polynomial Lasso Programs [chapter]

Jan Leike, Ashish Tiwari
2014 Lecture Notes in Computer Science  
We present a method for the synthesis of polynomial lasso programs.  ...  This constraint is non-linear and is passed to an SMT solver.  ...  Acknowledgements We would like to thank the anonymous reviewers for their valuable feedback.  ... 
doi:10.1007/978-3-642-54013-4_24 fatcat:zk5owyarqrfd7grbm6i3mloqz4

Non Linear Temporal Textures Synthesis: A Monte Carlo Approach [chapter]

Andrea Masiero, Alessandro Chiuso
2006 Lecture Notes in Computer Science  
Extending upon recent work which is available in the literature, we tackle the synthesis using non-linear dynamical models.  ...  The non-linear model is never given explicitly but rather we describe a methodology to generate samples from the model.  ...  This appear to be a difficult task for general non linear dynamical models f (x t , w t ).  ... 
doi:10.1007/11744047_22 fatcat:2i7tz64jq5hlplhh3r6nrz2jdm

Algebra-based Loop Synthesis [article]

Andreas Humenberger, Laura Kovács
2020 arXiv   pre-print
We present an algorithm for synthesizing program loops satisfying a given polynomial loop invariant.  ...  We turn the task of loop synthesis into a polynomial constraint problem by precisely characterizing the set of all loops satisfying the given invariant.  ...  Conclusions We proposed a syntax-guided synthesis procedure for synthesizing loops from a given polynomial loop invariant.  ... 
arXiv:2004.11787v2 fatcat:kqv4fjdwjrfmblbtahpumidgem

Quantum Particle Swarm Optimization for Synthesis of Non-uniformly Spaced Linear Arrays with Broadband Frequency Invariant Pattern

Hemant Patidar, Gautam Kumar Mahanti, R Muralidharan
2017 Journal of Microwaves, Optoelectronics and Electromagnetic Applications  
This paper describes a method using Quantum Particle Swarm Optimization to obtain a broadband frequency invariant pattern for synthesis of nonuniformly spaced linear array of isotropic antennas.  ...  Even though, the developed method is utilized here for a linear array of isotropic antennas; it can be extended to other type of arrays.  ...  APPROACH FOR FREQUENCY INVARIANT PATTERN SYNTHESIS A non-uniformly spaced linear array of 2N isotropic antennas along Y-axis has been considered.  ... 
doi:10.1590/2179-10742017v16i3790 fatcat:5ufynwukvjdo3g6q77i6qhmwle

Linear Invariants for Linear Systems [article]

Ashish Tiwari
2021 arXiv   pre-print
We say a system has a k linear invariant, k-LI in short, if it has a conjunction of k linear (non-strict) inequalities – equivalently, an intersection of k (closed) half spaces – as an invariant.  ...  Our result enables analysis of continuous and hybrid systems with linear dynamics in their modes solely using reasoning in the theory of linear arithmetic (polygons), without needing reasoning over nonlinear  ...  The synthesis problem asks us to generate the invariant for the given linear system. Definition 5 (2s-LI Synthesis Problem).  ... 
arXiv:2107.09642v1 fatcat:ozom34oswbhoxlm5whrkf3gn2u

Linear Ranking for Linear Lasso Programs [article]

Matthias Heizmann, Jochen Hoenicke, Jan Leike, Andreas Podelski
2014 arXiv   pre-print
The termination argument for a lasso program is a pair of a ranking function and an invariant.  ...  The completeness theorem establishes that, even though we use only linear (as opposed to non-linear) constraint solving, we are able to compute termination arguments in several interesting cases.  ...  The step from 'non-linear' to 'linear' is interesting for principled reasons (non-linear arithmetic constraint solving is undecidable in the case of integers).  ... 
arXiv:1401.5347v1 fatcat:h6plykinjncjxatu4yuzbiq7wy

Linear Ranking for Linear Lasso Programs [chapter]

Matthias Heizmann, Jochen Hoenicke, Jan Leike, Andreas Podelski
2013 Lecture Notes in Computer Science  
The termination argument for a lasso program is a pair of a ranking function and an invariant.  ...  The completeness theorem establishes that, even though we use only linear (as opposed to non-linear) constraint solving, we are able to compute termination arguments in several interesting cases.  ...  The step from 'non-linear' to 'linear' is interesting for principled reasons (non-linear arithmetic constraint solving is undecidable in the case of integers).  ... 
doi:10.1007/978-3-319-02444-8_26 fatcat:lueu7svi6nhklgnr44kxsakx4e

Counterexample- and Simulation-Guided Floating-Point Loop Invariant Synthesis [chapter]

Anastasiia Izycheva, Eva Darulova, Helmut Seidl
2020 Lecture Notes in Computer Science  
Such invariants are a prerequisite for reasoning about the safety and roundoff errors of floating-point programs.  ...  AbstractWe present an automated procedure for synthesizing sound inductive invariants for floating-point numerical loops.  ...  We would like to thank Sebastian Bruggisser for helping to debug our ellipsoids.  ... 
doi:10.1007/978-3-030-65474-0_8 fatcat:g62rmena2ranrmrobp6jmwqhde

From program verification to program synthesis

Saurabh Srivastava, Sumit Gulwani, Jeffrey S. Foster
2010 Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '10  
This paper describes a novel technique for the synthesis of imperative programs.  ...  Our synthesis algorithm works by creating a program with unknown statements, guards, inductive invariants, and ranking functions.  ...  We would also like to thank Avik Chaudhuri, Elnatan Reisner, and the other anonymous reviewers, for their invaluable feedback.  ... 
doi:10.1145/1706299.1706337 dblp:conf/popl/SrivastavaGF10 fatcat:2xgo5gg6wjdlrkks74dkdddf5a

From program verification to program synthesis

Saurabh Srivastava, Sumit Gulwani, Jeffrey S. Foster
2010 SIGPLAN notices  
This paper describes a novel technique for the synthesis of imperative programs.  ...  Our synthesis algorithm works by creating a program with unknown statements, guards, inductive invariants, and ranking functions.  ...  We would also like to thank Avik Chaudhuri, Elnatan Reisner, and the other anonymous reviewers, for their invaluable feedback.  ... 
doi:10.1145/1707801.1706337 fatcat:bedkyxss3nd3fiho4ztus7rkk4
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