“A la Floyd” induction principles for proving inevitability
Algebraic methods in semantics
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
Abstract interpretation and application to logic programs
Journal of Logic Programming
Approximating the domains of functional and imperative programs
Science of Computer Programming
An axiomatic basis for computer programming
Communications of the ACM
Automatic discovery of linear restraints among variables of a program
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Introduction to Mathematical Theory of Computation
Introduction to Mathematical Theory of Computation
Systematic design of program analysis frameworks
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Discovering affine equalities using random interpretation
POPL '03 Proceedings of the 30th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Synthesis of Linear Ranking Functions
TACAS 2001 Proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Termination analysis of integer linear loops
CONCUR 2005 - Concurrency Theory
Termination proofs for systems code
Proceedings of the 2006 ACM SIGPLAN conference on Programming language design and implementation
Integrating static analysis and general-purpose theorem proving for termination analysis
Proceedings of the 28th international conference on Software engineering
Variance analyses from invariance analyses
Proceedings of the 34th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Proving that programs eventually do something good
Proceedings of the 34th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Proceedings of the 2007 ACM SIGPLAN conference on Programming language design and implementation
Proceedings of the 2007 ACM SIGPLAN conference on Programming language design and implementation
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Recurrence with affine level mappings is p-time decidable for clp$({\mathbb r})$
Theory and Practice of Logic Programming
Program analysis as constraint solving
Proceedings of the 2008 ACM SIGPLAN conference on Programming language design and implementation
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Dependency Analysis for Control Flow Cycles in Reactive Communicating Processes
SPIN '08 Proceedings of the 15th international workshop on Model Checking Software
Endomorphisms for Non-trivial Non-linear Loop Invariant Generation
Proceedings of the 5th international colloquium on Theoretical Aspects of Computing
Automatic modular abstractions for linear constraints
Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
Theoretical Computer Science
A termination analyzer for Java bytecode based on path-length
ACM Transactions on Programming Languages and Systems (TOPLAS)
A minimalistic look at widening operators
Higher-Order and Symbolic Computation
A sound and complete proof rule for region stability of hybrid systems
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
The constraint database approach to software verification
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
Constraint solving for interpolation
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
Invariant synthesis for combined theories
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
CDB-PV: a constraint database-based program verifier
SARA'07 Proceedings of the 7th International conference on Abstraction, reformulation, and approximation
Discovering non-linear ranking functions by solving semi-algebraic systems
ICTAC'07 Proceedings of the 4th international conference on Theoretical aspects of computing
Region stability proofs for hybrid systems
FORMATS'07 Proceedings of the 5th international conference on Formal modeling and analysis of timed systems
Generating polynomial invariants with DISCOVERER and QEPCAD
Formal methods and hybrid real-time systems
Constraint solving for interpolation
Journal of Symbolic Computation
Static Analysis by Abstract Interpretation: A Mathematical Programming Approach
Electronic Notes in Theoretical Computer Science (ENTCS)
Multi-dimensional rankings, program termination, and complexity bounds of flowchart programs
SAS'10 Proceedings of the 17th international conference on Static analysis
Linear-invariant generation for probabilistic programs: automated support for proof-based methods
SAS'10 Proceedings of the 17th international conference on Static analysis
Solving systems of rational equations through strategy iteration
ACM Transactions on Programming Languages and Systems (TOPLAS)
Improving strategies via SMT solving
ESOP'11/ETAPS'11 Proceedings of the 20th European conference on Programming languages and systems: part of the joint European conferences on theory and practice of software
Interprocedurally analyzing polynomial identities
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Integrating physical systems in the static analysis of embedded control software
APLAS'05 Proceedings of the Third Asian conference on Programming Languages and Systems
An abstract interpretation framework for termination
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Verification constraint problems with strengthening
ICTAC'06 Proceedings of the Third international conference on Theoretical Aspects of Computing
Termination of loop programs with polynomial guards
ICCSA'10 Proceedings of the 2010 international conference on Computational Science and Its Applications - Volume Part IV
Termination analysis with calling context graphs
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Verifying the incorrectness of programs and automata
SARA'05 Proceedings of the 6th international conference on Abstraction, Reformulation and Approximation
Global optimization of polynomials restricted to a smooth variety using sums of squares
Journal of Symbolic Computation
Generation of basic semi-algebraic invariants using convex polyhedra
SAS'05 Proceedings of the 12th international conference on Static Analysis
Abstraction refinement for termination
SAS'05 Proceedings of the 12th international conference on Static Analysis
Proving liveness by backwards reachability
CONCUR'06 Proceedings of the 17th international conference on Concurrency Theory
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
A region graph based approach to termination proofs
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
A generic ellipsoid abstract domain for linear time invariant systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
A new look at the automatic synthesis of linear ranking functions
Information and Computation
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Precise enforcement of progress-sensitive security
Proceedings of the 2012 ACM conference on Computer and communications security
Symbolic termination analysis of solvable loops
Journal of Symbolic Computation
Termination proofs for linear simple loops
SAS'12 Proceedings of the 19th international conference on Static Analysis
On the linear ranking problem for integer linear-constraint loops
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Word-length optimization beyond straight line code
Proceedings of the ACM/SIGDA international symposium on Field programmable gate arrays
Proceedings of the 2013 9th Joint Meeting on Foundations of Software Engineering
Probabilistic program analysis with martingales
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
Synthesizing switching controllers for hybrid systems by generating invariants
Theories of Programming and Formal Methods
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In order to verify semialgebraic programs, we automatize the Floyd/Naur/Hoare proof method. The main task is to automatically infer valid invariants and rank functions. First we express the program semantics in polynomial form. Then the unknown rank function and invariants are abstracted in parametric form. The implication in the Floyd/Naur/Hoare verification conditions is handled by abstraction into numerical constraints by Lagrangian relaxation. The remaining universal quantification is handled by semidefinite programming relaxation. Finally the parameters are computed using semidefinite programming solvers. This new approach exploits the recent progress in the numerical resolution of linear or bilinear matrix inequalities by semidefinite programming using efficient polynomial primal/dual interior point methods generalizing those well-known in linear programming to convex optimization. The framework is applied to invariance and termination proof of sequential, nondeterministic, concurrent, and fair parallel imperative polynomial programs and can easily be extended to other safety and liveness properties.