Avoiding exponential explosion: generating compact verification conditions
POPL '01 Proceedings of the 28th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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
PPCP '94 Proceedings of the Second International Workshop on Principles and Practice of Constraint Programming
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Non-linear loop invariant generation using Gröbner bases
Proceedings of the 31st 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
Inferring Min and Max Invariants Using Max-Plus Polyhedra
SAS '08 Proceedings of the 15th international symposium on Static Analysis
Constraint-Based Approach for Analysis of Hybrid Systems
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Hard problems in max-algebra, control theory, hypergraphs and other areas
Information Processing Letters
From program verification to program synthesis
Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
An improved tight closure algorithm for integer octagonal constraints
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
ESOP'08/ETAPS'08 Proceedings of the Theory and practice of software, 17th European conference on Programming languages and systems
Termination of linear programs with nonlinear constraints
Journal of Symbolic Computation
Synthesis of loop-free programs
Proceedings of the 32nd ACM SIGPLAN conference on Programming language design and implementation
Verification and synthesis using real quantifier elimination
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Synthesis of optimal switching logic for hybrid systems
EMSOFT '11 Proceedings of the ninth ACM international conference on Embedded software
Synthesizing switching logic using constraint solving
International Journal on Software Tools for Technology Transfer (STTT) - VMCAI 2009
A scalable method for solving satisfiability of integer linear arithmetic logic
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
ESOP'05 Proceedings of the 14th European conference on Programming Languages and Systems
RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
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Geometric heuristics for the quantifier elimination approach presented by Kapur (2004) are investigated to automatically derive loop invariants expressing weakly relational numerical properties (such as l≤x≤h or l≤±x ±y≤h) for imperative programs. Such properties have been successfully used to analyze commercial software consisting of hundreds of thousands of lines of code (using for example, the Astrée tool based on abstract interpretation framework proposed by Cousot and his group). The main attraction of the proposed approach is its much lower complexity in contrast to the abstract interpretation approach (O(n2) in contrast to O(n4), where n is the number of variables) with the ability to still generate invariants of comparable strength. This approach has been generalized to consider disjunctive invariants of the similar form, expressed using maximum function (such as max (x+a,y+b,z+c,d)≤max (x+e,y+f,z+g,h)), thus enabling automatic generation of a subclass of disjunctive invariants for imperative programs as well.