Regular Realizability Problems and Context-Free Languages

We consider a computational model which is known as set automata. The set automata are one-way finite automata with an additional storage the set. There are two kinds of set automata the deterministic and the nondeterministic ones. We denote them as DSA and NSA respectively. The model was introduced by M. Kutrib, A. Malcher, M. Wendlandt in 2014 in [3] and [4]. It was shown that DSA-languages look similar to DCFL due to their closure properties and NSA-languages look similar to CFL due to their undecidability properties. In this paper, which is an extended version of the conference paper [10], we show that this similarity is natural: we prove that languages recognizable by NSA form a rational cone, so as CFL. The main topic of this paper is computational complexity: we prove that -languages recognizable by DSA belong to P and there are P-complete languages among them; -languages recognizable by NSA are in NP and there are NP-complete languages among them; -the word membership problem is P-complete for DSA without ε-loops and PSPACE-complete for general DSA; -the emptiness problem is in PSPACE for NSA and, moreover, it is PSPACE-complete for DSA.

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“…The language R I is specified by Eq. (9). Such a representation has polynomial size, namely, O(n 2 ).…”

Section: Proof Of Lemma 21mentioning

confidence: 99%

“…Note that rational transductions preserve regularity [1]: T M (Σ * ) ∈ REG. It is shown in [9] that an NFA recognizing T M (Σ * ) is log-space constructible by the description of T M . So (L(M ) ?…”

Section: The Emptiness Problem and The Regular Realizability Problemmentioning

confidence: 99%

On Computational Complexity of Set Automata

Rubtsov

Vyalyi

2017

Developments in Language Theory

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“…A variant of our intersection non-emptiness problem was studied in [30]. There, a context-free language L is fixed, a (deterministic or non-deterministic) finite automaton A is the input, and the question is, whether L ∩ L(A) = ∅ holds.…”

Section: Further Related Workmentioning

confidence: 99%

Circuit Evaluation for Finite Semirings

Ganardi¹,

Hucke²,

König³

et al. 2016

Preprint

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The computational complexity of the circuit evaluation problem for finite semirings is considered, where semirings are not assumed to have an additive or multiplicative identity. The following dichotomy is shown: If a finite semiring is such that (i) the multiplicative semigroup is solvable and (ii) it does not contain a subsemiring with an additive identity 0 and a multiplicative identity 1 = 0, then the circuit evaluation problem for the semiring is in DET ⊆ NC 2 . In all other cases, the circuit evaluation problem is P-complete.

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“…For instance, the Datalog program in Example 1 is linear. Many efforts have been devoted to find larger subclasses of context-free languages (Datalog programs) having the polynomial rational indices [1,2,5,9,30,31,32]. Two equivalent classes generalizing linear languages were proposed: piecewise linear programs [9,31] and the family of quasi-rational languages (the substitution closure of the family of linear languages) [5]; both were independently shown to have the polynomial rational index.…”

Section: Introductionmentioning

confidence: 99%

Rational index of bounded-oscillation languages

Shemetova¹,

Okhotin²,

Grigorev³

2020

Preprint

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The rational index of a context-free language L is a function f (n), such that for each regular language R recognized by an automaton with n states, the intersection of L and R is either empty or contains a word shorter than f (n). It is known that the context-free language (CFL-)reachability problem and Datalog query evaluation for context-free languages (queries) with the polynomial rational index is in NC, while these problems is P-complete in the general case. We investigate the rational index of bounded-oscillation languages and show that it is of polynomial order. We obtain upper bounds on the values of the rational index for general bounded-oscillation languages and for some of its previously studied subclasses.

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Regular Realizability Problems and Context-Free Languages

Cited by 10 publications

References 24 publications

On Computational Complexity of Set Automata

On Computational Complexity of Set Automata

Circuit Evaluation for Finite Semirings

Rational index of bounded-oscillation languages

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