Countable nondeterminism and random assignment
Journal of the ACM (JACM)
A generalization of the differential approach to recursive query evaluation
Journal of Logic Programming
Precise interprocedural dataflow analysis via graph reachability
POPL '95 Proceedings of the 22nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Precise interprocedural dataflow analysis with applications to constant propagation
TAPSOFT '95 Selected papers from the 6th international joint conference on Theory and practice of software development
Finite Differencing of Computable Expressions
ACM Transactions on Programming Languages and Systems (TOPLAS)
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
Constructive design of a hierarchy of semantics of a transition system by abstract interpretation
Theoretical Computer Science
Program Flow Analysis: Theory and Application
Program Flow Analysis: Theory and Application
Discovering affine equalities using random interpretation
POPL '03 Proceedings of the 30th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Propagating differences: an efficient new fixpoint algorithm for distributive constraint systems
Nordic Journal of Computing
Polynomial Constants Are Decidable
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
The Interprocedural Coincidence Theorem
CC '92 Proceedings of the 4th International Conference on Compiler Construction
Constraint-based inter-procedural analysis of parallel programs
Nordic Journal of Computing
Static determination of dynamic properties of generalized type unions
Proceedings of an ACM conference on Language design for reliable software
Weighted pushdown systems and their application to interprocedural dataflow analysis
SAS'03 Proceedings of the 10th international conference on Static analysis
Precise widening operators for convex polyhedra
SAS'03 Proceedings of the 10th international conference on Static analysis
Computing polynomial program invariants
Information Processing Letters
Precise interprocedural analysis using random interpretation
Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Weighted pushdown systems and their application to interprocedural dataflow analysis
Science of Computer Programming - Special issue: Static analysis symposium (SAS 2003)
LTL Over integer periodicity constraints
Theoretical Computer Science
Automatic generation of polynomial invariants of bounded degree using abstract interpretation
Science of Computer Programming
Polynomial approximations of the relational semantics of imperative programs
Science of Computer Programming
Generating all polynomial invariants in simple loops
Journal of Symbolic Computation
Whole-program linear-constant analysis with applications to link-time optimization
SCOPES '07 Proceedingsof the 10th international workshop on Software & compilers for embedded systems
Analysis of modular arithmetic
ACM Transactions on Programming Languages and Systems (TOPLAS) - Special Issue ESOP'05
Generating precise and concise procedure summaries
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Program analysis as constraint solving
Proceedings of the 2008 ACM SIGPLAN conference on Programming language design and implementation
Logical Interpretation: Static Program Analysis Using Theorem Proving
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Reducing Concurrent Analysis Under a Context Bound to Sequential Analysis
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Certification Using the Mobius Base Logic
Formal Methods for Components and Objects
SubPolyhedra: A (More) Scalable Approach to Infer Linear Inequalities
VMCAI '09 Proceedings of the 10th International Conference on Verification, Model Checking, and Abstract Interpretation
Equivalence Checking of Static Affine Programs Using Widening to Handle Recurrences
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Reducing concurrent analysis under a context bound to sequential analysis
Formal Methods in System Design
Invariant Checking for Programs with Procedure Calls
SAS '09 Proceedings of the 16th International Symposium on Static Analysis
A Smooth Combination of Linear and Herbrand Equalities for Polynomial Time Must-Alias Analysis
FM '09 Proceedings of the 2nd World Congress on Formal Methods
Grids: a domain for analyzing the distribution of numerical values
LOPSTR'06 Proceedings of the 16th international conference on Logic-based program synthesis and transformation
Computing procedure summaries for interprocedural analysis
ESOP'07 Proceedings of the 16th European conference on Programming
Interprocedurally analysing linear inequality relations
ESOP'07 Proceedings of the 16th European conference on Programming
Program analysis using weighted pushdown systems
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
CC'08/ETAPS'08 Proceedings of the Joint European Conferences on Theory and Practice of Software 17th international conference on Compiler construction
Efficient context-sensitive shape analysis with graph based heap models
CC'08/ETAPS'08 Proceedings of the Joint European Conferences on Theory and Practice of Software 17th international conference on Compiler construction
Interprocedural analysis of concurrent programs under a context bound
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Upper adjoints for fast inter-procedural variable equalities
ESOP'08/ETAPS'08 Proceedings of the Theory and practice of software, 17th European conference on Programming languages and systems
Generating polynomial invariants with DISCOVERER and QEPCAD
Formal methods and hybrid real-time systems
Invariant generation for P-solvable loops with assignments
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
Polynomial invariants for linear loops
Cybernetics and Systems Analysis
Electronic Notes in Theoretical Computer Science (ENTCS)
Points-to analysis as a system of linear equations
SAS'10 Proceedings of the 17th international conference on Static analysis
Certified result checking for polyhedral analysis of bytecode programs
TGC'10 Proceedings of the 5th international conference on Trustworthly global computing
Reference count analysis with shallow aliasing
Information Processing Letters
Static analysis of interrupt-driven programs synchronized via the priority ceiling protocol
Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Interprocedural control flow reconstruction
APLAS'10 Proceedings of the 8th Asian conference on Programming languages and systems
Solving systems of rational equations through strategy iteration
ACM Transactions on Programming Languages and Systems (TOPLAS)
An iterative method for generating loop invariants
FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Side-effect analysis of assembly code
SAS'11 Proceedings of the 18th international conference on Static analysis
Abstract domains of affine relations
SAS'11 Proceedings of the 18th international conference on Static analysis
Fast interprocedural linear two-variable equalities
ACM Transactions on Programming Languages and Systems (TOPLAS)
Interprocedurally analyzing polynomial identities
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Linearity analysis for automatic differentiation
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part IV
An abstract domain to discover interval linear equalities
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
Checking herbrand equalities and beyond
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Counterexamples with loops for predicate abstraction
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
On the computational complexity of dynamic slicing problems for program schemas
Mathematical Structures in Computer Science - Programming Language Interference and Dependence
Analysis of modular arithmetic
ESOP'05 Proceedings of the 14th European conference on Programming Languages and Systems
ESOP'05 Proceedings of the 14th European conference on Programming Languages and Systems
Extended weighted pushdown systems
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Generation of basic semi-algebraic invariants using convex polyhedra
SAS'05 Proceedings of the 12th international conference on Static Analysis
A generic framework for interprocedural analysis of numerical properties
SAS'05 Proceedings of the 12th international conference on Static Analysis
Join algorithms for the theory of uninterpreted functions
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Path optimization in programs and its application to debugging
ESOP'06 Proceedings of the 15th European conference on Programming Languages and Systems
Assertion checking over combined abstraction of linear arithmetic and uninterpreted functions
ESOP'06 Proceedings of the 15th European conference on Programming Languages and Systems
Equivalence checking of static affine programs using widening to handle recurrences
ACM Transactions on Programming Languages and Systems (TOPLAS)
Precise relational invariants through strategy iteration
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Modular static analysis with zonotopes
SAS'12 Proceedings of the 19th international conference on Static Analysis
ICFEM'12 Proceedings of the 14th international conference on Formal Engineering Methods: formal methods and software engineering
TSL: A System for Generating Abstract Interpreters and its Application to Machine-Code Analysis
ACM Transactions on Programming Languages and Systems (TOPLAS)
Probabilistic program analysis with martingales
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
Counterexample-guided abstraction refinement for linear programs with arrays
Automated Software Engineering
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We apply linear algebra techniques to precise interprocedural dataflow analysis. Specifically, we describe analyses that determine for each program point identities that are valid among the program variables whenever control reaches that program point. Our analyses fully interpret assignment statements with affine expressions on the right hand side while considering other assignments as non-deterministic and ignoring conditions at branches. Under this abstraction, the analysis computes the set of all affine relations and, more generally, all polynomial relations of bounded degree precisely. The running time of our algorithms is linear in the program size and polynomial in the number of occurring variables. We also show how to deal with affine preconditions and local variables and indicate how to handle parameters and return values of procedures.