Algorithmic decomposition of shuffle on words

Biegler, Franziska; Daley, Mark; McQuillan, Ian

doi:10.1016/j.tcs.2012.04.001

Cited by 6 publications

(10 citation statements)

References 4 publications

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“…Moreover, this algorithm runs in time O(|u| + |v|), which is sublinear in the input M . This main result from [16] is as follows: Proposition 6. Let M be an acyclic, trim, non-unary DFA over Σ.…”

Section: Comparing Shuffle On Words To Nfasmentioning

confidence: 96%

“…To obtain the following corollary, it only needs to be shown that the problem is in NP, which again follows from Corollary 2 and Proposition 3. It is known that there is a polynomial-time algorithm that, given a DFA, will output two words u and v such that, if L(M ) is decomposable into the shuffle of two words, then this implies L(M ) = u v [16]. Moreover, this algorithm runs in time O(|u| + |v|), which is sublinear in the input M .…”

Section: Comparing Shuffle On Words To Nfasmentioning

confidence: 99%

“…A known result involving shuffle on words is that there is a polynomial-time test to determine, given words u, v ∈ Σ + and a DFA M , whether u v ⊆ L(M ) [16]. An alternate simpler proof of this result is demonstrated next, and then this proof technique will be used to extend to more general decision problems.…”

Section: Testing Inclusion Of the Shuffle Of Languages In Another Lanmentioning

confidence: 99%

“…In this paper, problems are investigated involving three given languages R, L 1 , L 2 , and the goal is to determine decidability and complexity of testing if R ⊆ L 1 L 2 , L 1 L 2 ⊆ R, and L 1 L 2 = R, depending on the language families of L 1 , L 2 and R. In Section 3, it is demonstrated that the following three problems are NP-complete: to determine, given an NFA M and two words u, v whether u v ⊆ L(M ) is true, L(M ) ⊆ u v is true, and u v = L(M ) is true. Then, the DFA algorithm from [16] that can output a "candidate solution" is extended to an algorithm on NFAs that operates in polynomial time, and outputs two words u, v such that if the NFA is decomposable into the shuffle of words, then u v is the unique solution. And in Section 4, decidability and the complexity of testing if L 1 L 2 ⊆ R is investigated involving more general language families.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On the Complexity and Decidability of Some Problems Involving Shuffle

Eremondi

Ibarra

McQuillan

2015

Descriptional Complexity of Formal Systems

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The complexity and decidability of various decision problems involving the shuffle operation (denoted by ) are studied. The following three problems are all shown to be NP-complete: given a nondeterministic finite automaton (NFA) M , and two words u and v, isIt is also shown that there is a polynomial-time algorithm to determine, for NFAs M 1 , M 2 , and a deterministic pushdown automaton M 3 , whether L(M 1 ) L(M 2 ) ⊆ L(M 3 ). The same is true when M 1 , M 2 , M 3 are one-way nondeterministic l-reversal-bounded k-counter machines, with M 3 being deterministic. Other decidability and complexity results are presented for testing whether given languages L 1 , L 2 , and R from various languages families satisfy L 1 L 2 ⊆ R, and R ⊆ L 1 L 2 . Several closure results on shuffle are also shown.

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Section: Comparing Shuffle On Words To Nfasmentioning

confidence: 96%

Section: Comparing Shuffle On Words To Nfasmentioning

confidence: 99%

Section: Testing Inclusion Of the Shuffle Of Languages In Another Lanmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the Complexity and Decidability of Some Problems Involving Shuffle

Eremondi

Ibarra

McQuillan

2015

Descriptional Complexity of Formal Systems

Self Cite

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show abstract

“…It appears that the latter approaches are inappropriate in terms of time consumption. Moreover, the language decompositions and primality problem are also studied in [2,4,5,12].…”

Section: Introductionmentioning

confidence: 99%

A prime decomposition algorithm for supercodes

Kieu¹

2014

JCC

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Tóm tắt. Siêu mã, một loại mã độ dài thay đổi có nhiều tính chất đặc biệt, đã được giới thiệu và nghiên cứu bởi Đỗ Long Vân và tác giả trong một số bài báo gần đây. Một siêu mã được gọi là nguyên tố nếu nó không thể phân tích thành tích ghép của hai siêu mã khác. Phân tích nguyên tố đối với một siêu mã là phân tích nó thành tích ghép của các siêu mã nguyên tố. Trong bài báo này, một thuật toán phân tích nguyên tố đối với các siêu mã có độ phức tạp tuyến tính đã được đề xuất. Tính duy nhất của việc phân tích một siêu mã thành một tích ghép duy nhất các siêu mã nguyên tố cũng được chứng minh.Từ khóa. Mã, siêu mã, siêu mã nguyên tố, phân tích nguyên tố.Abstract. Supercode, a particular case of hypercodes, has been introduced and considered by D. L. Van and the author in previous papers. A supercode is called prime if it cannot be decomposed as a catenation of two supercodes. The prime decomposition of a supercode L is to decompose L into prime supercodes. In this paper, a linear-time prime decomposition algorithm for supercodes is proposed. The uniqueness of the prime decomposition for supercodes is presented.

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On Comparing Deterministic Finite Automata and the Shuffle of Words

Biegler

McQuillan

2014

Implementation and Application of Automata

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Algorithmic decomposition of shuffle on words

Cited by 6 publications

References 4 publications

On the Complexity and Decidability of Some Problems Involving Shuffle

On the Complexity and Decidability of Some Problems Involving Shuffle

A prime decomposition algorithm for supercodes

On Comparing Deterministic Finite Automata and the Shuffle of Words

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