On the NP-completeness of cryptarithms

@article{Epstein1987OnTN,
  title={On the NP-completeness of cryptarithms},
  author={Dick Epstein},
  journal={SIGACT News},
  year={1987},
  volume={18},
  pages={38-40}
}
  • D. Epstein
  • Published 1 April 1987
  • Philosophy
  • SIGACT News
If we only consider problems with decimal numbers as above there is no possibility of any hardness result, because there are only 10! different assignments of digits and letters to try. Therefore we will generalize the problem slightly: the base of representation for our numbers will be given as part of the problem (expressed in unary or binary) rather than always being decimal, and we will allow the puzzle to contain arbitrarily many different letters (up to the base of representation). The… 
View on ACM
dl.acm.org
21 Citations
Highly Influential Citations
2
Background Citations
11

21 Citations

Enumeration of Cryptarithms Using Deterministic Finite Automata

The method to construct a DFA that accepts cryptarithms that admit (unique) solutions for each base is implemented and a D FA for bases \(k \le 7\) is constructed.

Enumerating Cryptarithms Using Deterministic Finite Automata

The method to construct a DFA that accepts cryptarithms that admit (unique) solutions for each base is implemented and a D FA for bases $k \le 7$ is constructed.

NP-completeness of Arithmetical Restorations

The NP-completeness of a problem deciding whether a given instance of arithmetical restorations of multiplication sums has a solution or not is shown.

Complexity and Completeness of Finding Another Solution and Its Application to Puzzles

This paper considers n-ASP, the problem to find another solution when n solutions are given, and considers ASP-completeness, the completeness with respect to the parsimonious reductions which allow polynomial-time transformation.

On Reconfiguration Problems: Structure and Tractability

Given an n-vertex graph G and two vertices s and t in G, determining whether there exists a path and computing the length of the shortest path between s and t are two of the most fundamental graph…

Games, puzzles and computation

This thesis develops the idea of game as computation to a greater degree than has been done previously, and presents a general family of games, called Constraint Logic, which is both mathematically simple and ideally suited for reductions to many actual board games.

A Survey of NP-Complete Puzzles

This article surveys NP-Complete puzzles in the hope of motivating further research in this fascinating area, particularly for those puzzles which have received little scientific attention to date.

Cryptarithms: A Non-Programming Approach Using Excel

This paper presents a method for solving cryptarithms using Microsoft Excel along with the Solver add-in, and introduces users of Excel to the often neglected integer and alldifferent constraints, as well as the increase in computational time associated with these constraints.

Playing Games with Algorithms: Algorithmic Combinatorial Game Theory

Background in combinatorial game theory is reviewed, which analyzes ideal play in perfect-information games and results about the complexity of determining ideal play are surveyed, in terms of both polynomial-time algorithms and computational intractability results.

Experience with a New Distributed Termination Detection Algorithm

The constraint based puzzle-solving method is explained, several test cases are reported, and preliminary experimental results show that far less control messages than indicated by the worst case behavior are usually generated.

References

SHOWING 1-6 OF 6 REFERENCES

Computers and Intractability: A Guide to the Theory of NP-Completeness

It is proved here that the number ofrules in any irredundant Horn knowledge base involving n propositional variables is at most n 0 1 times the minimum possible number of rules.

Artificial Intelligence

The history, the major landmarks, and some of the controversies in each of these twelve topics are discussed, as well as some predictions about the course of future research.

Madachy's Mathematical Recreations

Computers and In stractability: A Guide to the Theory of NP-Completeness. W. H Freeman, San Fran

Report Inst

  • Theory of Numbers, University of Colorado, Boulder
  • 1959

Computers and Intractibility : A Guide to the Theory o f NP-Completeness

  • Computers and Intractibility : A Guide to the Theory o f NP-Completeness
  • 1979