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Non-linear reasoning for invariant synthesis

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. ...

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

2021
*
Lecture Notes in Computer Science
*

We first describe an algorithmic approach

doi:10.1007/978-3-030-67067-2_2
fatcat:mzjf6jjlgndu3ehhiwv4v4w7oi
*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. ...##
###
Schema-Guided Synthesis of Imperative Programs by Constraint Solving
[chapter]

2005
*
Lecture Notes in Computer Science
*

We present a method

doi:10.1007/11506676_11
fatcat:v5g3mlrhxffmrmpv23gtdbew5a
*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] . ...##
###
Preliminary Notes on Termination and Non-Termination Reasoning
[article]

2013
*
arXiv
*
pre-print

In this preliminary note, we will illustrate our ideas on automated mechanisms

arXiv:1309.3128v1
fatcat:2z26ygbs3zghxkn77opyxrceme
*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 ...##
###
Synthesis for Polynomial Lasso Programs
[article]

2013
*
arXiv
*
pre-print

We present a method

arXiv:1311.4046v1
fatcat:t3o2mz4az5gmrj2zwb2ejihnh4
*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. ...##
###
Synthesis for Polynomial Lasso Programs
[chapter]

2014
*
Lecture Notes in Computer Science
*

We present a method

doi:10.1007/978-3-642-54013-4_24
fatcat:zk5owyarqrfd7grbm6i3mloqz4
*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. ...##
###
Non Linear Temporal Textures Synthesis: A Monte Carlo Approach
[chapter]

2006
*
Lecture Notes in Computer Science
*

Extending upon recent work which is available in the literature, we tackle the

doi:10.1007/11744047_22
fatcat:2i7tz64jq5hlplhh3r6nrz2jdm
*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 ). ...##
###
Algebra-based Loop Synthesis
[article]

2020
*
arXiv
*
pre-print

We present an algorithm

arXiv:2004.11787v2
fatcat:kqv4fjdwjrfmblbtahpumidgem
*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*. ...##
###
Quantum Particle Swarm Optimization for Synthesis of Non-uniformly Spaced Linear Arrays with Broadband Frequency Invariant Pattern

2017
*
Journal of Microwaves, Optoelectronics and Electromagnetic Applications
*

This paper describes a method using Quantum Particle Swarm Optimization to obtain a broadband frequency

doi:10.1590/2179-10742017v16i3790
fatcat:5ufynwukvjdo3g6q77i6qhmwle
*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. ...##
###
Linear Invariants for Linear Systems
[article]

2021
*
arXiv
*
pre-print

We say a system has a k

arXiv:2107.09642v1
fatcat:ozom34oswbhoxlm5whrkf3gn2u
*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). ...##
###
Linear Ranking for Linear Lasso Programs
[article]

2014
*
arXiv
*
pre-print

The termination argument

arXiv:1401.5347v1
fatcat:h6plykinjncjxatu4yuzbiq7wy
*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). ...##
###
Linear Ranking for Linear Lasso Programs
[chapter]

2013
*
Lecture Notes in Computer Science
*

The termination argument

doi:10.1007/978-3-319-02444-8_26
fatcat:lueu7svi6nhklgnr44kxsakx4e
*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). ...##
###
Counterexample- and Simulation-Guided Floating-Point Loop Invariant Synthesis
[chapter]

2020
*
Lecture Notes in Computer Science
*

Such

doi:10.1007/978-3-030-65474-0_8
fatcat:g62rmena2ranrmrobp6jmwqhde
*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. ...##
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From program verification to program synthesis

2010
*
Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '10
*

This paper describes a novel technique

doi:10.1145/1706299.1706337
dblp:conf/popl/SrivastavaGF10
fatcat:2xgo5gg6wjdlrkks74dkdddf5a
*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. ...##
###
From program verification to program synthesis

2010
*
SIGPLAN notices
*

This paper describes a novel technique

doi:10.1145/1707801.1706337
fatcat:bedkyxss3nd3fiho4ztus7rkk4
*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. ...
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