State Complexity of Insertion

Theoretical Computer Science

2019

Self Cite

The paper investigates the closure of the language family defined by input-driven pushdown automata (IDPDA) under the following operations: insertion ins(L, K) = {xyz | xz ∈ L, y ∈ K}, deletion del(L, K) = {xz | xyz ∈ L, y ∈ K}, square root √ L = {w | ww ∈ L}, and the first half 1 2 L = {u | ∃v : |u| = |v|, uv ∈ L}. For K and L recognized by nondeterministic IDPDA, with m and with n states, respectively, insertion requires mn + 2m states, as long as K is well-nested; deletion is representable with 2n states, for well-nested K; square root requires n 3 −O(n 2) states, for well-nested L; the well-nested subset of the first half is representable with 2 O(n 2) states. Without the well-nestedness constraints, non-closure is established in each case.

Section: Insertionmentioning

confidence: 98%

Section: Insertionmentioning

confidence: 99%

See 1 more Smart Citation

Further closure properties of input-driven pushdown automata

Okhotin

Theoretical Computer Science

2019

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“…To conclude, we consider the nondeterministic state complexity of these operations. The upper bound is the same as the bound for the nondeterministic state complexity of ordinary insertion [11], however, the construction used for Lemma 4 is not the same. Using Lemma 1 (the fooling set lemma [1]) we can establish a matching lower bound.…”

Section: Decision Problems For Maximal/minimal Sdimentioning

confidence: 99%

Site-Directed Insertion: Decision Problems, Maximality and Minimality

Cho

Han

Descriptional Complexity of Formal Systems

et al. 2018

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Site-directed insertion is an overlapping insertion operation that can be viewed as analogous to the overlap assembly or chop operations that concatenate strings by overlapping a suffix and a prefix of the argument strings. We consider decision problems and language equations involving site-directed insertion. By relying on the tools provided by semantic shuffle on trajectories we show that one variable equations involving site-directed insertion and regular constants can be solved. We consider also maximal and minimal variants of the site-directed insertion operation.

“…For finite automata, the closure under this operation is folklore, and its precise state complexity has recently been determined by Han et al [8]. For input-driven automata, the closure is currently known only for singleton K [22].…”

Section: Introductionmentioning

confidence: 99%

Further Closure Properties of Input-Driven Pushdown Automata

Okhotin

Descriptional Complexity of Formal Systems

2018

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The paper investigates the closure of the language family defined by input-driven pushdown automata (IDPDA) under the following operations: insertion ins(L, K)For K and L recognized by nondeterministic IDPDA, with m and with n states, respectively, insertion requires mn + 2m states, as long as K is well-nested; deletion is representable with 2n states, for well-nested K; square root requires n 3 −O(n 2 ) states, for well-nested L; the well-nested subset of the first half is representable with 2 O(n 2 ) states. Without the well-nestedness constraints, non-closure is established in each case.