© 1999 AI Access Foundation and Morgan Kaufmann Publishers. All rights reserved.

**
Tad Hogg
Xerox Palo Alto Research Center
3333 Coyote Hill Road, Palo Alto, CA 94304
hogg@parc.xerox.com
**

A previously developed quantum search algorithm for solving 1-SAT
problems in a single step is generalized to apply to a range of
highly constrained *k*-SAT problems. We identify a bound on the
number of clauses in satisfiability problems for which the
generalized algorithm can find a solution in a constant number of
steps as the number of variables increases. This performance
contrasts with the linear growth in the number of steps required
by the best classical algorithms, and the exponential number
required by classical and quantum methods that ignore the problem
structure. In some cases, the algorithm can also guarantee that
insoluble problems in fact have no solutions, unlike previously
proposed quantum search algorithms.

- 1 Introduction
- 2 Quantum Computers
- 3 The Satisfiability Problem
- 4 Solving 1-SAT
- 5 Applying the Algorithm to
*k*-SAT - 6 Solving Maximally Constrained
*k*-SAT - 7 Solving Highly Constrained Random
*k*-SAT - 8 Discussion
- References
- About this document ...

Feb. 1999