Determining the Equivalence of Algebraic Expressions by Hash Coding
Journal of the ACM (JACM)
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Probabilistic Algorithms for Deciding Equivalence of Straight-Line Programs
Journal of the ACM (JACM)
Algebraic simplification: a guide for the perplexed
Communications of the ACM
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
New results for random determination of equivalence of expressions
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
A system for manipulating polynomials given by straight-line programs
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
Using types as search keys in function libraries
FPCA '89 Proceedings of the fourth international conference on Functional programming languages and computer architecture
The design of a user interface to a computer algebra system for introductory calculus
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Signature functions for algebraic numbers
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Dagwood: a system for manipulating polynomials given by straight-line programs
ACM Transactions on Mathematical Software (TOMS)
Equality in computer algebra and beyond
Journal of Symbolic Computation - Integrated reasoning and algebra systems
Algebraic simplification of GP programs during evolution
Proceedings of the 8th annual conference on Genetic and evolutionary computation
Genetic programming for medical classification: a program simplification approach
Genetic Programming and Evolvable Machines
Online program simplification in genetic programming
SEAL'06 Proceedings of the 6th international conference on Simulated Evolution And Learning
Hierarchical representations with signatures for large expression management
AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
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We devise several procedures based on signatures (or hashing functions) to determine equivalence of expressions in Random Polynomial Time (also called Probabilistic Polynomial Time) (RPT). These procedures return as result: “equivalent” or “not-equivalent”. The result “not-equivalent” is always correct, while the result “equivalent” is correct with probability at least 1-&egr;. This probability depends on a random number generator and is independent of the problem being solved. In all our procedures, the value &egr; can be made arbitrarily small. This method works for determining equivalence over an important class of functions as well as answering other questions like linearity, polynomial dependence, squareness, independence, etc.