TY - JOUR

T1 - Further closure properties of input-driven pushdown automata

AU - Okhotin, Alexander

AU - Salomaa, Kai

PY - 2019/12/17

Y1 - 2019/12/17

N2 - 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}, the first half [Formula presented] and cyclic shift (Figure presented.). For K and L recognized by nondeterministic IDPDA, with m and with n states, respectively, insertion requires exactly mn+2m states, as long as K is well-nested; deletion requires exactly 2n states, for well-nested K; square root requires n3−O(n2) states, for well-nested L; the well-nested subset of the first half is representable with 2O(n2) states; the well-nested subset of the cyclic shift requires exactly 2n2 states. Without the well-nestedness constraints, non-closure is established in each case.

AB - 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}, the first half [Formula presented] and cyclic shift (Figure presented.). For K and L recognized by nondeterministic IDPDA, with m and with n states, respectively, insertion requires exactly mn+2m states, as long as K is well-nested; deletion requires exactly 2n states, for well-nested K; square root requires n3−O(n2) states, for well-nested L; the well-nested subset of the first half is representable with 2O(n2) states; the well-nested subset of the cyclic shift requires exactly 2n2 states. Without the well-nestedness constraints, non-closure is established in each case.

KW - Cyclic shift

KW - Deletion

KW - Input-driven automata

KW - Insertion

KW - Proportional removals

KW - Square root

KW - Visibly pushdown automata

UR - http://www.scopus.com/inward/record.url?scp=85067178569&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2019.04.006

DO - 10.1016/j.tcs.2019.04.006

M3 - Article

AN - SCOPUS:85067178569

VL - 798

SP - 65

EP - 77

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -