Algorithms for maximal existential and universal width Algorithms for maximal existential and universal width

Maximal existential width and maximal universal width provide methods of quantifying the amount of nondeterminism and parallelism, respectively, present in computations of an alternating finite automaton (AFA). In this paper, we primarily seek to understand the complexity landscape of the problems p...

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Veröffentlicht in:	Natural computing Jg. 24; H. 3; S. 541 - 556
Hauptverfasser:	Alajaji, John, Salomaa, Kai
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Dordrecht Springer Netherlands 01.09.2025 Springer Nature B.V
Schlagworte:	Algorithms Artificial Intelligence Complex Systems Computation Computer Science Evolutionary Biology Integers Leaves Polynomials Processor Architectures Theory of Computation Trees Alternating finite automaton Measure of nondeterminism Decidability Universal and existential choices
ISSN:	1567-7818, 1572-9796
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Abstract	Maximal existential width and maximal universal width provide methods of quantifying the amount of nondeterminism and parallelism, respectively, present in computations of an alternating finite automaton (AFA). In this paper, we primarily seek to understand the complexity landscape of the problems pertaining to computing these widths. One such problem involves deciding whether the maximal universal width or maximal existential width of an AFA is bounded by a given integer k . For the case of a nondeterministic finite automaton (NFA), we give a polynomial time algorithm for computing maximal existential width. We also present a polynomial time algorithm for computing the existential width of a general AFA, under the assumption that the AFA’s universal width is bounded by a fixed integer ℓ . Finally, we reconsider the problems of computing existential and universal widths for AFAs over a unary language and demonstrate that both problems can be solved in polynomial time.
AbstractList	Maximal existential width and maximal universal width provide methods of quantifying the amount of nondeterminism and parallelism, respectively, present in computations of an alternating finite automaton (AFA). In this paper, we primarily seek to understand the complexity landscape of the problems pertaining to computing these widths. One such problem involves deciding whether the maximal universal width or maximal existential width of an AFA is bounded by a given integer k. For the case of a nondeterministic finite automaton (NFA), we give a polynomial time algorithm for computing maximal existential width. We also present a polynomial time algorithm for computing the existential width of a general AFA, under the assumption that the AFA’s universal width is bounded by a fixed integer ℓ. Finally, we reconsider the problems of computing existential and universal widths for AFAs over a unary language and demonstrate that both problems can be solved in polynomial time. Maximal existential width and maximal universal width provide methods of quantifying the amount of nondeterminism and parallelism, respectively, present in computations of an alternating finite automaton (AFA). In this paper, we primarily seek to understand the complexity landscape of the problems pertaining to computing these widths. One such problem involves deciding whether the maximal universal width or maximal existential width of an AFA is bounded by a given integer k . For the case of a nondeterministic finite automaton (NFA), we give a polynomial time algorithm for computing maximal existential width. We also present a polynomial time algorithm for computing the existential width of a general AFA, under the assumption that the AFA’s universal width is bounded by a fixed integer ℓ . Finally, we reconsider the problems of computing existential and universal widths for AFAs over a unary language and demonstrate that both problems can be solved in polynomial time.
Author	Alajaji, John Salomaa, Kai
Author_xml	– sequence: 1 givenname: John surname: Alajaji fullname: Alajaji, John email: 18ja19@queensu.ca organization: School of Computing, Queen’s University – sequence: 2 givenname: Kai surname: Salomaa fullname: Salomaa, Kai organization: School of Computing, Queen’s University
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Cites_doi	10.1007/978-3-319-62809-7_23 10.1016/0890-5401(90)90053-K 10.1016/0304-3975(86)90142-8 10.1007/BF00263994 10.1007/s002360050133 10.1016/j.tcs.2024.114506 10.1017/CBO9780511808876 10.1007/978-3-030-62536-8_8 10.5555/3173440.3173451 10.1137/0218083 10.1145/322234.322243 10.1006/inco.2001.3069 10.1007/978-981-19-0957-3 10.1007/978-3-030-93489-7_8 10.7561/SACS.2023.1.53 10.1007/978-3-642-59126-6 10.1007/978-3-031-34326-1_4 10.1109/SWAT.1971.10
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References	A John (10022_CR1) 2024; 1045 A Palioudakis (10022_CR15) 2012; 17 J Hromkovič (10022_CR8) 2002; 172 CMR Kintala (10022_CR13) 1980; 13 M Zakzok (10022_CR22) 2024 J Goldstine (10022_CR6) 1990; 86 10022_CR9 AK Chandra (10022_CR2) 1981; 28 M Sipser (10022_CR19) 2013 C Keeler (10022_CR11) 2021 G Pighizzini (10022_CR16) 2017 B Ravikumar (10022_CR17) 1989; 18 H Yo-Sub (10022_CR7) 2023 TH Cormen (10022_CR5) 2009 H Leung (10022_CR14) 1998; 35 C Keeler (10022_CR12) 2023; 33 10022_CR20 S Yu (10022_CR21) 1997 10022_CR10 J Shallit (10022_CR18) 2008 S Cioaba (10022_CR4) 2022 M Chrobak (10022_CR3) 1986; 47
References_xml	– start-page: 308 volume-title: Developments in language theory year: 2017 ident: 10022_CR16 doi: 10.1007/978-3-319-62809-7_23 – volume: 86 start-page: 179 issue: 2 year: 1990 ident: 10022_CR6 publication-title: Inf Comput doi: 10.1016/0890-5401(90)90053-K – volume-title: Introduction to the theory of computation year: 2013 ident: 10022_CR19 – volume: 47 start-page: 149 issue: 2 year: 1986 ident: 10022_CR3 publication-title: Theor Comput Sci doi: 10.1016/0304-3975(86)90142-8 – volume: 13 start-page: 199 year: 1980 ident: 10022_CR13 publication-title: Acta Inf doi: 10.1007/BF00263994 – volume: 35 start-page: 595 issue: 7 year: 1998 ident: 10022_CR14 publication-title: Acta Inf doi: 10.1007/s002360050133 – year: 2024 ident: 10022_CR22 publication-title: Theor Comput Sci doi: 10.1016/j.tcs.2024.114506 – volume-title: Introduction to algorithms year: 2009 ident: 10022_CR5 – volume-title: A second course in formal languages and automata theory year: 2008 ident: 10022_CR18 doi: 10.1017/CBO9780511808876 – ident: 10022_CR10 doi: 10.1007/978-3-030-62536-8_8 – volume: 17 start-page: 245 issue: 2–4 year: 2012 ident: 10022_CR15 publication-title: J Automata Lang Comb doi: 10.5555/3173440.3173451 – volume: 18 start-page: 1263 issue: 6 year: 1989 ident: 10022_CR17 publication-title: SIAM J Comput doi: 10.1137/0218083 – volume: 1045 issue: 1 year: 2024 ident: 10022_CR1 publication-title: Theor Comput Sci – volume: 28 start-page: 114 issue: 1 year: 1981 ident: 10022_CR2 publication-title: J ACM doi: 10.1145/322234.322243 – volume: 172 start-page: 202 year: 2002 ident: 10022_CR8 publication-title: Inf Comput doi: 10.1006/inco.2001.3069 – volume-title: A first course in graph theory and combinatorics year: 2022 ident: 10022_CR4 doi: 10.1007/978-981-19-0957-3 – start-page: 88 volume-title: Descriptional complexity of formal systems year: 2021 ident: 10022_CR11 doi: 10.1007/978-3-030-93489-7_8 – volume: 33 start-page: 53 issue: 1 year: 2023 ident: 10022_CR12 publication-title: Sci Ann Comput Sci doi: 10.7561/SACS.2023.1.53 – start-page: 41 volume-title: Handbook of formal languages year: 1997 ident: 10022_CR21 doi: 10.1007/978-3-642-59126-6 – start-page: 51 volume-title: Descriptional complexity of formal systems year: 2023 ident: 10022_CR7 doi: 10.1007/978-3-031-34326-1_4 – ident: 10022_CR20 doi: 10.1109/SWAT.1971.10 – ident: 10022_CR9
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SubjectTerms	Algorithms Artificial Intelligence Complex Systems Computation Computer Science Evolutionary Biology Integers Leaves Polynomials Processor Architectures Theory of Computation Trees
Subtitle	Algorithms for maximal existential and universal width
Title	Algorithms for maximal existential and universal width
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