Automatic recognition of induction variables and recurrence relations by abstract interpretation
PLDI '90 Proceedings of the ACM SIGPLAN 1990 conference on Programming language design and implementation
A Mathematica version of Zeilberger's algorithm for proving binomial coefficient identities
Journal of Symbolic Computation - Special issue on symbolic computation in combinatorics
The Mathematica Book
Symbolic summation with single-nested sum extensions
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Automatic Derivation of Loop Bounds and Infeasible Paths for WCET Analysis Using Abstract Execution
RTSS '06 Proceedings of the 27th IEEE International Real-Time Systems Symposium
The design and implementation of VAMPIRE
AI Communications - CASC
Static Loop Bound Analysis of C Programs Based on Flow Analysis and Abstract Interpretation
RTCSA '08 Proceedings of the 2008 14th IEEE International Conference on Embedded and Real-Time Computing Systems and Applications
SPEED: precise and efficient static estimation of program computational complexity
Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Valigator: A Verification Tool with Bound and Invariant Generation
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Boolector: An Efficient SMT Solver for Bit-Vectors and Arrays
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'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
The reachability-bound problem
PLDI '10 Proceedings of the 2010 ACM SIGPLAN conference on Programming language design and implementation
Closed-Form Upper Bounds in Static Cost Analysis
Journal of Automated Reasoning
ABC: algebraic bound computation for loops
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
Beyond loop bounds: comparing annotation languages for worst-case execution time analysis
Software and Systems Modeling (SoSyM)
r-TuBound: loop bounds for WCET analysis (tool paper)
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
FFX: a portable WCET annotation language
Proceedings of the 20th International Conference on Real-Time and Network Systems
The WCET analysis tool calcwcet167
ISoLA'12 Proceedings of the 5th international conference on Leveraging Applications of Formal Methods, Verification and Validation: applications and case studies - Volume Part II
Abstract acceleration of general linear loops
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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We present an automatic method for computing tight upper bounds on the iteration number of special classes of program loops. These upper bounds are further used in the WCET analysis of programs. To do so, we refine program flows using SMT reasoning and rewrite multi-path loops into single-path ones. Single-path loops are further translated into a set of recurrence relations over program variables. Recurrence relations are solved and iteration bounds of program loops are derived from the computed closed forms. For solving recurrences we deploy a pattern-based recurrence solving algorithm and compute closed forms only for a restricted class of recurrence equations. However, in practice, these recurrences describe the behavior of a large set of program loops. Our technique is implemented in the r-TuBound tool and was successfully tried out on a number of challenging WCET benchmarks.