What is the best-known method of elimination for the extended class?

The best-known decision procedure for it (described by Kreisel and Krevine [9], among others) is based on a method of elimination of variables.

how can i make a qpairs function grow faster?

for example, a table is used to record the results o f internal calls, the amount of work reqmred to compute EQPAIRS can be made to grow no faster than the square of the length of the input.

How many axioms are generated for each pair of terms?

each axiom at least triples the n u m b e r of ILP's that must be solved m deciding the reduced formula/~.Suppose, for example, that the axiom x = y D f ( x ) = f l y ) is generated m step (2).

Open AccessJournal Article10.1145/322123.322137

A Practical Decision Procedure for Arithmetic with Function Symbols

Robert E. Shostak

- 01 Apr 1979

- Journal of the ACM

- Vol. 26, Iss: 2, pp 351-360

201

TL;DR: A practical procedure is presented for an extension of quantifier-free Presburger arithmetic that permits arbitrary unmterpreted predicate and function symbols and is powerful enough to encode the semantics of array operators as well as MAX, MIN, and ABSVALUE.

Abstract: A practical procedure is presented for an extension of quantifier-free Presburger arithmetic that permits arbitrary unmterpreted predicate and function symbols This theory includes many of the formulas one tends to encounter in program venficatlon and is powerful enough to encode the semantics of array operators as well as MAX, MIN, and ABSVALUE An implementation of the procedure has proved to be of great value in a program verlficauon system developed at SRI for the United States Air Force

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Most frequently asked questions

1. What are the contributions in "A practical decision procedure for arithmetic with function symbols" ?

A practical procedure is presented for an extension of quantifier-free Presburger arithmetic that permits arbitrary unmterpreted predicate and function symbols

2. What is the first stage of the formula F to be decided?

In the first stage the formula F to be decided is reduced to a set of integer linear programming problems (ILP's) with the property that F is vahd if and only if none of the problems has a solution.

3. How do the authors get the n-ary function symbol from the extended class?

Using step (1) to el iminate the uninterpreted funct ion symbol P, the authors obta in the formula F ' gwen byl(f~(z) = 0 D z = 1) A g(y) = z + 41 D The authorf ( g ( Y ) ) = f ( 3 + 2z) Vfp ( l ) # 0l.

4. How can The authorsolve a g iven?

I f the ILP solver used can be operated incremental ly (as can simplex-based methods), the new ILP's can be solved with little addmona l effort.

Citations

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- 01 Sep 1988

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References

•Journal Article•10.1090/S0002-9904-1958-10224-4

Outline of an algorithm for integer solutions to linear programs

Ralph E. Gomory

- 01 Sep 1958

- Bulletin of the American Mathematical So...

1.3K

Book Chapter•10.1007/978-94-011-1793-7_2

Towards a Mathematical Science of Computation

John J. McCarthy

- 01 Jan 1993

- Journal of Symbolic Logic

TL;DR: The prospects for a mathematical science of computation is discussed and it is shown that from Newton’s law of gravitation and his laws of motion, one can deduce that the planetary orbits obey Kepler's laws.

...read moreread less

589

•Proceedings Article

Towards a Mathematical Science of Computation.

John J. McCarthy

- 01 Jan 1962

TL;DR: In this paper, the authors discuss the prospects for a mathematical science of computation, and discuss the basic assumptions of the entities treated by the science, such as Newton's law of gravitation and Kepler's laws of motion.

...read moreread less

468

•Journal Article•10.1016/0022-0000(78)90021-1

A 222pn upper bound on the complexity of Presburger Arithmetic

Derek C. Oppen

- 01 Jun 1978

- Journal of Computer and System Sciences

TL;DR: The decision problem for the theory of integers under addition, or “Presburger Arithmetic,” is proved to be elementary recursive in the sense of Kalmar and it is proved that a quantifier elimination decision procedure for this theory determines the truth of any sentence of length n within deterministic time.

...read moreread less

205

Journal Article•10.1145/359545.359570

An algorithm for reasoning about equality

Robert E. Shostak

- 01 Jul 1978

- Communications of The ACM

TL;DR: A simple technique for reasoning about equalities that is fast and complete for ground formulas with function symbols and equality is presented.

...read moreread less

146

A Practical Decision Procedure for Arithmetic with Function Symbols

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AI Agents for this Paper

Most frequently asked questions

1. What are the contributions in "A practical decision procedure for arithmetic with function symbols" ?

2. What is the first stage of the formula F to be decided?

3. How do the authors get the n-ary function symbol from the extended class?

4. How can The authorsolve a g iven?

5. What is the best-known method of elimination for the extended class?

6. how can i make a qpairs function grow faster?

7. How many axioms are generated for each pair of terms?

Citations

CHAPTER 6 – Rewrite Systems

Satisfiability Modulo Theories

Formal verification in hardware design: a survey

Lazy Satisfiability Modulo Theories

Integrating decision procedures into heuristic theorem provers: a case study of linear arithmetic

References

Outline of an algorithm for integer solutions to linear programs

Towards a Mathematical Science of Computation

Towards a Mathematical Science of Computation.

A 222pn upper bound on the complexity of Presburger Arithmetic

An algorithm for reasoning about equality

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