Minimal NFA problems are hard

Jiang, Tao; Ravikumar, Bala

doi:10.1007/3-540-54233-7_169

Cited by 68 publications

(82 citation statements)

References 15 publications

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“…Finally, we let s = 3n + 18m + k. Now, we only need to show that G has a vertex cover of size at most k if and only if the edge-RMP problem has a solution with |UA| + |PA| at most s. The intuitive idea behind the proof follows the proof idea of Jiang and Ravikumar [10]: to describe the user u having permission {x i , y i }, the set of roles, ROLES must have either the role {x i , y i } or the two roles {x i } and {y i }. In the first situation |UA| + |PA| = 1 + 2 = 3.…”

Section: Theorem 1 the Decision Edge Rmp Is Np-completementioning

confidence: 95%

“…Interestingly, to the best of our knowledge, most (if not all) of the prior NP-complete problems try to find some variant of the minimum number of roles/cliques/vertices satisfying some condition (we have not been able to find one that corresponds to edges). Nevertheless, we augment and use the NP-completeness proof given for the normal set basis problem by Jiang and Ravikumar [10].…”

Section: Complexitymentioning

confidence: 98%

“…find the column of the biggest edge-key (including redundant constraints) 6: {for columns of the same edge-key, choose the one whose corresponding role has the fewest permissions} 7: Let c ij contributing to satisfying constraints and d j of the chosen column be 1 8: end for 9: Delete the constraints being satisfied. 10 The nine cells of the left matrix (given by the multiplication of the two depicted matrices on the left hand side) correspond to nine constraints, denoted by {x ij , 1 i 3, 1 j 3}. By step 2, we determine that {c 13 , c 14 , c 22 , c 24 } are 0.…”

Section: A Greedy Algorithm For Edge-rmpmentioning

confidence: 99%

“…Let |E | = m . Jiang and Ravikumar make the following observation [10]: for any e ∈ E at least four sets from ROLES are required (in addition to the sets c i , c j {x i }, and {x j }) to cover the users u 1 i,j , . .…”

Section: Theorem 1 the Decision Edge Rmp Is Np-completementioning

confidence: 99%

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Edge-RMP: Minimizing administrative assignments for role-based access control

Vaidya

Atluri

Guo

et al. 2009

JCS

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Because of its ease of administration, role-based access control (RBAC) has become the norm to enforcing security in most of today's organizations. For implementing RBAC, it is important to devise a complete and correct set of roles. This task, known as role engineering, has been identified as one of the costliest components in deploying RBAC. A key problem with respect to role engineering is that there is no formal metric for measuring the goodness/interestingness of the devised set of roles. Recently, Vaidya et al. [26], formally define the role mining problem (RMP) as the problem of discovering an optimal set of roles from existing user permissions, and analyze its theoretical bounds. Essentially, given a userpermission assignment (UPA), the basic RMP is to discover the user-role assignment relation (UA) and role-permission assignment relation (PA) such that the number of roles required is minimum. In this paper, we present another interesting and useful problem, called the edge-RMP, with a different minimality objective. The edge-RMP, requires the discovery of a complete and correct set of roles such that the discovered |UA|+|PA| is the minimum possible. Minimal |UA|+|PA| is a useful metric as it would minimize the administrative burden since less number of assignments need to be managed. Although the basic-RMP and the edge-RMP appear to be related problems, we demonstrate with concrete examples that they are, in fact, independent of each other. We prove that the edge-RMP is an NP-hard problem by reducing the known "vertex cover problem" to the decision version of the edge-RMP. Another important contribution of this paper is to provide a binary integer programming solution to this problem by showing that the edge-RMP can be formulated in that form. As a result, one can directly borrow existing implementation solutions for binary integer programming and guide further research in this direction. We also propose a heuristic solution for large scale problems, and experimentally validate our algorithm.

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Section: Theorem 1 the Decision Edge Rmp Is Np-completementioning

confidence: 95%

Section: Complexitymentioning

confidence: 98%

Section: A Greedy Algorithm For Edge-rmpmentioning

confidence: 99%

Section: Theorem 1 the Decision Edge Rmp Is Np-completementioning

confidence: 99%

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Edge-RMP: Minimizing administrative assignments for role-based access control

Vaidya

Atluri

Guo

et al. 2009

JCS

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“…Since, it was proved in [28] that we can obtain a polynomial algorithm for minimizing DFAs, and in [19] was proved that an O(n log n) algorithm exists. In the meantime, several heuristic approaches have been proposed to reduce the size of NFAs [2,21], and it was proved by Jiang and Ravikumar [22] that NFA minimization problems are hard; even in case of regular languages over a one letter alphabet, the minimization is NP-complete [13,22].…”

Section: Introductionmentioning

confidence: 99%

Non-Deterministic Finite Cover Automata

Câmpeanu¹

2015

SACS

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The concept of Deterministic Finite Cover Automata (DFCA) was introduced at WIA '98, as a more compact representation than Deterministic Finite Automata (DFA) for finite languages. In some cases representing a finite language using a Non-deterministic Finite Automata (NFA) may significantly reduce the number of required states. The combined power of the succinctness of the representation of finite languages using both cover languages and non-determinism has been suggested, but never systematically studied. In the present paper, for non-deterministic finite cover automata (NFCA) and l-nondeterministic finite cover automaton (l-NFCA), we show that minimization can be as hard as minimizing NFAs for regular languages, even in the case of NFCAs using unary alphabets. Moreover, we show how we can adapt the methods used to reduce, or minimize the size of NFAs/DFCAs/l-DFCAs, for simplifying NFCAs/l-NFCAs.

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