Journal of Information Technology Services (한국IT서비스학회지)

Korea Society of IT Services (한국IT서비스학회)
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Algorithm for Computing J Relations in the Monoid of Boolean Matrices

불리언 행렬의 모노이드에서의 J 관계 계산 알고리즘

  • 한재일 (국민대학교 전자정보통신대학 컴퓨터공학부)
  • Published : 2008.12.31
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Abstract

Green's relations are five equivalence relations that characterize the elements of a semigroup in terms of the principal ideals. The J relation is one of Green's relations. Although there are known algorithms that can compute Green relations, they are not useful for finding all J relations in the semigroup of all $n{\times}n$ Boolean matrices. Its computation requires multiplication of three Boolean matrices for each of all possible triples of $n{\times}n$ Boolean matrices. The size of the semigroup of all $n{\times}n$ Boolean matrices grows exponentially as n increases. It is easy to see that it involves exponential time complexity. The computation of J relations over the $5{\times}5$ Boolean matrix is left an unsolved problem. The paper shows theorems that can reduce the computation time, discusses an algorithm for efficient J relation computation whose design reflects those theorems and gives its execution results.

Keywords

References

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