The polyranking principle

Authors:
Aaron R. Bradley;Zohar Manna;Henny B. Sipma
Affiliations:
Computer Science Department, Stanford University, Stanford, CA;Computer Science Department, Stanford University, Stanford, CA;Computer Science Department, Stanford University, Stanford, CA
Venue:
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Year:
2005

Citing 10
Cited 32

Theory of linear and integer programming

Theory of linear and integer programming
The size-change principle for program termination

POPL '01 Proceedings of the 28th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Visual Abstractions for Temporal Verification

AMAST '98 Proceedings of the 7th International Conference on Algebraic Methodology and Software Technology
Synthesis of Linear Ranking Functions

TACAS 2001 Proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Practical Methods for Proving Program Termination

CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Deductive Model Checking

CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
Transition Invariants

LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Proving program invariance and termination by parametric abstraction, lagrangian relaxation and semidefinite programming

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
Linear ranking with reachability

CAV'05 Proceedings of the 17th international conference on Computer Aided Verification

Variance analyses from invariance analyses

Proceedings of the 34th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Proving thread termination

Proceedings of the 2007 ACM SIGPLAN conference on Programming language design and implementation
Proving non-termination

Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Heap Assumptions on Demand

CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Proving Conditional Termination

CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
A Numerical Abstract Domain Based on Expression Abstraction and Max Operator with Application in Timing Analysis

CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
SPEED: precise and efficient static estimation of program computational complexity

Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A combination framework for tracking partition sizes

Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
SPEED: Symbolic Complexity Bound Analysis

CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Software model checking

ACM Computing Surveys (CSUR)
Sequential verification of serializability

Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Invariants for Parameterised Boolean Equation Systems

Theoretical Computer Science
Proving termination of tree manipulating programs

ATVA'07 Proceedings of the 5th international conference on Automated technology for verification and analysis
Termination of rewriting with right-flat rules

RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Multi-dimensional rankings, program termination, and complexity bounds of flowchart programs

SAS'10 Proceedings of the 17th international conference on Static analysis
Alternation for termination

SAS'10 Proceedings of the 17th international conference on Static analysis
Proving program termination

Communications of the ACM
Metric spaces and termination analyses

APLAS'10 Proceedings of the 8th Asian conference on Programming languages and systems
Temporal property verification as a program analysis task

CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Model checking of hybrid systems: from reachability towards stability

HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Verification constraint problems with strengthening

ICTAC'06 Proceedings of the Third international conference on Theoretical Aspects of Computing
Temporal property verification as a program analysis task

Formal Methods in System Design
Termination analysis with algorithmic learning

CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
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
Ramsey vs. lexicographic termination proving

TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Termination proofs from tests

Proceedings of the 2013 9th Joint Meeting on Foundations of Software Engineering
Reasoning about nondeterminism in programs

Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation
Eventual linear ranking functions

Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming
Proving termination starting from the end

CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
Better termination proving through cooperation

CAV'13 Proceedings of the 25th international conference on Computer Aided Verification

Quantified Score

Hi-index	0.02

Visualization

Abstract

Although every terminating loop has a ranking function, not every loop has a ranking function of a restricted form, such as a lexicographic tuple of polynomials over program variables. The polyranking principle is proposed as a generalization of polynomial ranking for analyzing termination of loops. We define lexicographic polyranking functions in the context of loops with parallel transitions consisting of polynomial assertions, including inequalities, over primed and unprimed variables. Next, we address synthesis of these functions with a complete and automatic method for synthesizing lexicographic linear polyranking functions with supporting linear invariants over linear loops.