On a class of languages with holonomic generating functions

Castiglione, Giuseppa; Massazza, Paolo

doi:10.1016/j.tcs.2016.07.022

Cited by 5 publications

(4 citation statements)

References 16 publications

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“…Finally, we will show an interesting language that is both context-free and strongly counting-regular. This language was presented in [31] as a member of the class RCM -a class defined as follows: RCM is the class of the languages given by < R, C, µ > where R is a regular language, C a system of linear constraints and µ, a length-preserving morphism that is injective on R ∩ [C]. The specific language we denote by L RCM is defined as follows:…”

Section: Verifies That For Eachmentioning

confidence: 99%

On counting functions and slenderness of languages

Ibarra

McQuillan

Ravikumar

2019

Theoretical Computer Science

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We study counting-regular languages -these are languages L for which there is a regular language L such that the number of strings of length n in L and L are the same for all n. We show that the languages accepted by unambiguous nondeterministic Turing machines with a one-way read-only input tape and a reversalbounded worktape are counting-regular. Many one-way acceptors are a special case of this model, such as reversal-bounded deterministic pushdown automata, reversal-bounded deterministic queue automata, and many others, and therefore all languages accepted by these models are counting-regular. This result is the best possible in the sense that the claim does not hold for either 2-ambiguous NPDA's, unambiguous NPDA's with no reversal-bound, and other models.We also study closure properties of counting-regular languages, and we study decidability problems in regards to counting-regularity. For example, it is shown that the counting-regularity of even some restricted subclasses of NPDA's is undecidable. Lastly, k-slender languages -where there are at most k words of any length -are also studied. Amongst other results, it is shown that it is decidable whether a language in any semilinear full trio is k-slender.

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Section: Verifies That For Eachmentioning

confidence: 99%

On counting functions and slenderness of languages

Ibarra

McQuillan

Ravikumar

2019

Theoretical Computer Science

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“…Despite their expressiveness, Parikh automata retain some decidability: nonemptiness, in particular, is NP-complete [12]. For weakly unambiguous Parikh automata, inclusion [7] and regular separability [8] are decidable as well. Figueira and Libkin [12] also argued that this model is well-suited for querying graph databases, while mitigating some of the complexity issues related with more expressive query languages.…”

Section: Introductionmentioning

confidence: 99%

History-deterministic Parikh Automata

Erlich¹,

Guha²,

Jecker³

et al. 2022

Preprint

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Parikh automata extend finite automata by counters that can be tested for membership in a semilinear set, but only at the end of a run. Thereby, they preserve many of the desirable properties of finite automata. Deterministic Parikh automata are strictly weaker than nondeterministic ones, but enjoy better closure and algorithmic properties.This state of affairs motivates the study of intermediate forms of nondeterminism. Here, we investigate history-deterministic Parikh automata, i.e., automata whose nondeterminism can be resolved on the fly. This restricted form of nondeterminism is well-suited for applications which classically call for determinism, e.g., solving games and composition.We show that history-deterministic Parikh automata are strictly more expressive than deterministic ones, incomparable to unambiguous ones, and enjoy almost all of the closure and some of the algorithmic properties of deterministic automata.

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“…In [11], it was shown that there is a polynomial time algorithm to decide, for fixed k, l whether the shuffle of two NCM(k, l) machines is contained in a DCM(k, l) machine. In addition, DCM was studied in [12] as part of an interesting conjecture involving holonomic functions. The authors define a family RCM that is obtained from the regular languages via so-called linear constraints on the number of occurrences of symbols, and homomorphisms.…”

Section: Introductionmentioning

confidence: 99%

“…It is demonstrated that all RCM languages have generating functions which are all holonomic functions. The class of holonomic functions in one variable is an extension of the algebraic functions which contains all those functions satisfying a linear differential equation with polynomial coefficients [12]. They conjectured that DCM is contained in RCM, implying that all DCM languages have holonomic generating functions.…”

Section: Introductionmentioning

confidence: 99%

Insertion operations on deterministic reversal-bounded counter machines

Eremondi

Ibarra

McQuillan

2019

Journal of Computer and System Sciences

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Several insertion operations are studied applied to languages accepted by one-way and two-way deterministic reversalbounded multicounter machines. These operations are defined by the ideals obtained from relations such as the prefix, infix, suffix, and outfix relations, as well as operations defined from inverses of a type of deterministic transducer with reversal-bounded counters attached. The question of whether the resulting languages can always be accepted by deterministic machines with the same number (or larger number) of input-turns (resp., counters, counter-reversals, etc.) is investigated.

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On a class of languages with holonomic generating functions

Cited by 5 publications

References 16 publications

On counting functions and slenderness of languages

On counting functions and slenderness of languages

History-deterministic Parikh Automata

Insertion operations on deterministic reversal-bounded counter machines

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