The Complexity of Regular(-Like) Expressions

Holzer, Markus; Kutrib, Martin

doi:10.1142/s0129054111008866

Cited by 10 publications

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“…Remark 6. Lemma 6.1 still holds if we extend regular expressions by a squaring operation ( 2 ) defined by L(R 2 ) := (L(R)) 2 as introduced in [35]; see also [36] for a more recent overview. To show this, proceed analogously to the case when R is a concatenation of two identical subexpressions R = R ′ • R ′ .…”

Section: Definition 61 (Log-product) a Homogeneous Expressionmentioning

confidence: 93%

Regular Expression Length via Arithmetic Formula Complexity

Cseresnyes

Seiwert

2020

Lecture Notes in Computer Science

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We prove lower bounds on the length of regular expressions for finite languages by methods from arithmetic circuit complexity. First, we show a reduction: the length of a regular expression for a language L ⊆ {0, 1} n is bounded from below by the minimum size of a monotone arithmetic formula computing a polynomial that has L as its set of exponent vectors, viewing words as vectors. This result yields lower bounds for the binomial language of all words with exactly k ones and n−k zeros and for the language of all Dyck words of length 2n. We also determine the blow-up of language operations (intersection and shuffle) of regular expressions for finite languages. Second, we adapt a lower bound method for multilinear arithmetic formulas by so-called log-product polynomials to regular expressions. With this method we show almost tight lower bounds for the language of all binary numbers with n bits that are divisible by a given odd integer p, for the language of all words of length n over a k letter alphabet with an even number of occurrences of each letter and for the language of all permutations of {1,. .. , n}.

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Section: Definition 61 (Log-product) a Homogeneous Expressionmentioning

confidence: 93%