An Automata Characterisation for Multiple Context-Free Languages

Denkinger, Tobias

doi:10.1007/978-3-662-53132-7_12

Cited by 7 publications

(7 citation statements)

References 11 publications

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“…MCF k : languages of k-multiple context-free grammars (see [29]); 5. RT SA k : languages of k-restricted tree stack automata (see [7]).…”

Section: Hyperedge Replacementmentioning

confidence: 99%

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Parallel Hyperedge Replacement String Languages

Campbell

2021

Electron. Proc. Theor. Comput. Sci.

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There are many open questions surrounding the characterisation of groups with context-sensitive word problem. Only in 2018 was it shown that all finitely generated virtually Abelian groups have multiple context-free word problems, and it is a long-standing open question as to where to place the word problems of hyperbolic groups in the formal language hierarchy. In this paper, we introduce a new language class called the parallel hyperedge replacement string languages, show that it contains all multiple context-free and ET0L languages, and lay down the foundations for future work that may be able to place the word problems of many hyperbolic groups in this class.

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“…MCF k : languages of k-multiple context-free grammars (see [29]); 5. RT SA k : languages of k-restricted tree stack automata (see [7]).…”

Section: Hyperedge Replacementmentioning

confidence: 99%

“…HRS k = HRS rf k for all k ≥ 2 is due to Theorem 2.2 and HRS rf 2k+1 ⊆ OUT(DT WT k ) ⊆ HRS 2k for all k ≥ 1 is due to Engelfriet et al [10], which gives us the equalities in (1) and (1) = (2). (2) = ( 3) is due to Weir [31], (3) = ( 4) is due to Seki et al (1991) [29], and (4) = ( 5) is due to Denkinger [7].…”

Section: Hyperedge Replacementmentioning

confidence: 99%

Parallel Hyperedge Replacement String Languages

Campbell

2021

Electron. Proc. Theor. Comput. Sci.

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“…MCF k : the languages of k-multiple context-free grammars (see [8]); 5. RT SA k : the languages of k-restricted tree stack automata (see [28]).…”

Section: Mcf Languagesmentioning

confidence: 99%

“…k for all k ≥ 2 is due to Theorem 2.12 and HRS rf 2k+1 ⊆ OUT(DT WT k ) ⊆ HRS 2k for all k ≥ 1 is due to Engelfriet and Heyker (1991) [9], which gives us the all the equalities in (1) and (1) = (2). (2) = (3) is due to Weir (1992) [10], (3) = ( 4) is due to Seki, Matsumura, Fujii, and Kasami (1991) [8], and (4) = ( 5) is due to Denkinger (2016) [28].…”

Section: Proof Hrs K = Hrs Rfmentioning

confidence: 99%

Parallel Hyperedge Replacement Grammars

Campbell

2021

Preprint

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In 2018, it was shown that all finitely generated virtually Abelian groups have multiple context-free word problems, and it is still an open problem as to where to precisely place the word problems of hyperbolic groups in the formal language hierarchy. Motivated by this, we introduce a new language class, the parallel hyperedge replacement string languages, containing all multiple context-free and ET0L languages. We show that parallel hyperedge replacement grammars can be "synchronised", which allows us to establish many useful formal language closure results relating to both the hypergraph and string languages generated by various families of parallel hyperedge replacement grammars, laying the foundations for future work in this area.

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“…Our starting point is the model of restricted tree-stack automata (rTSA) [8], known to be expressively equivalent to MAHORS [6] (with respect to tree generation). A tree-stack is a tree-shaped stack (growing upwards) satisfying restriction: each node can be visited from below no more than an a priori fixed number (𝑘, say) of times.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Verification Beyond Context-Freeness

Murawski

Ong

2022

Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science

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Probabilistic pushdown automata (recursive state machines) are a widely known model of probabilistic computation associated with many decidable problems concerning termination (time) and lineartime model checking. Higher-order recursion schemes (HORS) are a prominent formalism for the analysis of higher-order computation.Recent studies showed that, for the probabilistic variant of HORS, even the basic problem of determining whether a scheme terminates almost surely is undecidable. Moreover, the undecidability already holds for order-2 schemes (order-1 schemes are known to correspond to pushdown automata).Motivated by these results, we study restricted probabilistic treestack automata (rPTSA), which in the nondeterministic setting are known to characterise a proper extension of context-free languages, namely, the multiple context-free languages. We show that several verification problems, such as almost-sure termination, positive almost-sure termination and 𝜔-regular model checking are decidable for this class.At the level of higher-order recursion schemes, this corresponds to being able to verify a probabilistic version of MAHORS (which are a multiplicative-additive version of higher-order recursion schemes). MAHORS extend order-1 recursion schemes and are incomparable with order-2 schemes. CCS CONCEPTS• Theory of computation → Grammars and context-free languages; Probabilistic computation; Program verification. KEYWORDS probabilistic (affine additive) higher-order recursion schemes; restricted (probabilistic) tree stack automata; computing termination probability; deciding almost sure termination; first-order theory of the reals

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An Automata Characterisation for Multiple Context-Free Languages

Abstract: We introduce tree stack automata as a new class of automata with storage and identify a restricted form of tree stack automata that recognises exactly the multiple context-free languages.

Cited by 7 publications

References 11 publications

Parallel Hyperedge Replacement String Languages

Parallel Hyperedge Replacement String Languages

Parallel Hyperedge Replacement Grammars

Probabilistic Verification Beyond Context-Freeness

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