Theory of linear and integer programming
Theory of linear and integer programming
Temporal verification of reactive systems: safety
Temporal verification of reactive systems: safety
Automatic generation of invariants and intermediate assertions
Theoretical Computer Science - Special issue: principles and practice of constraint 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
Double Description Method Revisited
Selected papers from the 8th Franco-Japanese and 4th Franco-Chinese Conference on Combinatorics and Computer Science
Powerful Techniques for the Automatic Generation of Invariants
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
STeP: The Stanford Temporal Prover (Educational Release) User''s Manual
STeP: The Stanford Temporal Prover (Educational Release) User''s Manual
Abstraction in Software Model Checking: Principles and Practice (Tutorial Overview and Bibliography)
Proceedings of the 9th International SPIN Workshop on Model Checking of Software
Possibly Not Closed Convex Polyhedra and the Parma Polyhedra Library
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
Analyzing Fair Parametric Extended Automata
SAS '01 Proceedings of the 8th International Symposium on Static Analysis
Practical Methods for Proving Program Termination
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Inference of termination conditions for numerical loops in Prolog
Theory and Practice of Logic Programming
Transition predicate abstraction and fair termination
Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Transition predicate abstraction and fair termination
Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Termination analysis of integer linear loops
CONCUR 2005 - Concurrency Theory
Precise widening operators for convex polyhedra
Science of Computer Programming - Special issue: Static analysis symposium (SAS 2003)
Termination of Floating-Point Computations
Journal of Automated Reasoning
Higher-Order and Symbolic Computation
Variance analyses from invariance analyses
Proceedings of the 34th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Transition predicate abstraction and fair termination
ACM Transactions on Programming Languages and Systems (TOPLAS) - Special issue on POPL 2005
Program Verification by Using DISCOVERER
Verified Software: Theories, Tools, Experiments
WISE: Automated test generation for worst-case complexity
ICSE '09 Proceedings of the 31st International Conference on Software Engineering
Proving Termination of Integer Term Rewriting
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
Automata-Based Termination Proofs
CIAA '09 Proceedings of the 14th International Conference on Implementation and Application of Automata
ACM Computing Surveys (CSUR)
A Term Rewriting Approach to the Automated Termination Analysis of Imperative Programs
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Theoretical Computer Science
Refining the control structure of loops using static analysis
EMSOFT '09 Proceedings of the seventh ACM international conference on Embedded software
Automatic invariant generation for hybrid systems using ideal fixed points
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
Precise widening operators for convex polyhedra
SAS'03 Proceedings of the 10th international conference on Static analysis
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
Discovering non-linear ranking functions by solving semi-algebraic systems
ICTAC'07 Proceedings of the 4th international conference on Theoretical aspects of computing
Termination of linear programs with nonlinear constraints
Journal of Symbolic Computation
Switching logic synthesis for reachability
EMSOFT '10 Proceedings of the tenth ACM international conference on Embedded software
Multi-dimensional rankings, program termination, and complexity bounds of flowchart programs
SAS'10 Proceedings of the 17th international conference on Static analysis
Deriving numerical abstract domains via principal component analysis
SAS'10 Proceedings of the 17th international conference on Static analysis
A compositional method for deciding equivalence and termination of nondeterministic programs
IFM'10 Proceedings of the 8th international conference on Integrated formal methods
Communications of the ACM
Decision procedures for automating termination proofs
VMCAI'11 Proceedings of the 12th international conference on Verification, model checking, and abstract interpretation
Relational abstractions for continuous and hybrid systems
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
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
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Termination of polynomial programs
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Separating fairness and well-foundedness for the analysis of fair discrete systems
TACAS'05 Proceedings of the 11th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Summaries for while programs with recursion
ESOP'05 Proceedings of the 14th European conference on Programming Languages and Systems
Termination analysis with compositional transition invariants
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Schema-guided synthesis of imperative programs by constraint solving
LOPSTR'04 Proceedings of the 14th international conference on Logic Based Program Synthesis and Transformation
Linear ranking with reachability
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
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
Termination analysis of imperative programs using bitvector arithmetic
VSTTE'12 Proceedings of the 4th international conference on Verified Software: theories, tools, experiments
A new look at the automatic synthesis of linear ranking functions
Information and Computation
Discovering invariants via simple component analysis
Journal of Symbolic Computation
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
On the Termination of Integer Loops
ACM Transactions on Programming Languages and Systems (TOPLAS)
Symbolic termination analysis of solvable loops
Journal of Symbolic Computation
Non-termination sets of simple linear loops
ICTAC'12 Proceedings of the 9th international conference on Theoretical Aspects of Computing
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
Probabilistic program analysis with martingales
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
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Deductive verification of progress properties relies on finding ranking functions to prove termination of program cycles. We present an algorithm to synthesize linear ranking functions that can establish such termination. Fundamental to our approach is the representation of systems of linear inequalities and sets of linear expressions as polyhedral cones. This representation allows us to reduce the search for linear ranking functions to the computation of polars, intersections and projections of polyhedral cones, problems which have well-known solutions.