Commutative grammars: The complexity of uniform word problems

Huynh, Dung T.

doi:10.1016/s0019-9958(83)80022-9

Cited by 52 publications

(33 citation statements)

References 6 publications

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“…Context-free non-commutative P-complete [3,13,14,21,24] commutative NP-complete [4,11] Context-sensitive non-commutative PSPACE-complete [15] commutative PSPACE-complete [11] Exponent-sensitive commutative PSPACE-complete This paper…”

Section: Classmentioning

confidence: 99%

Completeness Results for Generalized Communication-Free Petri Nets with Arbitrary Edge Multiplicities

Mayr

Weihmann

2013

Lecture Notes in Computer Science

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We investigate gcf-Petri nets, a generalization of communication-free Petri nets allowing arbitrary edge multiplicities, and characterized by the sole restriction that each transition has at most one incoming edge. We use canonical ring sequences with nice properties for gcf-PNs to show that the RecLFS, (zero-)reachability, covering, and boundedness problems of gcf-PNs are in PSPACE. By showing, how PSPACE-Turing machines can be simulated by gss-PNs, a subclass of gcf-PNs where additionally all transitions have at most one outgoing edge, we ultimately prove the PSPACE-completess of these problems for gss/gcf-PNs. Then, we show PSPACE-hardness as well as a doubly exponential space bound for the containment, and equivalence problems of gss/gcf-PNs. Last, we consider a new natural generalization of context-free commutative grammars. Our results for gcf-PNs imply PSPACE-completeness for its uniform word problem.

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Section: Classmentioning

confidence: 99%

Completeness Results for Generalized Communication-Free Petri Nets with Arbitrary Edge Multiplicities

Mayr

Weihmann

2013

Lecture Notes in Computer Science

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“…The language (2.4) is not recognized by a stateless automaton, as shown in [17]. [21], see also [17]. One example is the commutative closure of the language of the previous example: the set of all words with the same number of occurrences of a, b and c.…”

Section: Multi-pushdown Automatamentioning

confidence: 99%

Reachability Problem for Weak Multi-Pushdown Automata

Czerwiński

Hofman

Lasota

2012

Lecture Notes in Computer Science

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Abstract. This paper is about reachability analysis in a restricted subclass of multipushdown automata. We assume that the control states of an automaton are partially ordered, and all transitions of an automaton go downwards with respect to the order. We prove decidability of the reachability problem, and computability of the backward reachability set. As the main contribution, we identify relevant subclasses where the reachability problem becomes NP-complete. This matches the complexity of the same problem for communication-free vector addition systems, a special case of stateless multipushdown automata.

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“…(1) (2) (3) Our work began with the question of describing the sequences of atomic actions performable by a flowchart algorithm which admits explicit nondeterminism and a forking type of parallelism. The kind of flowchart scheme is made precise below in our definition of a parallel transition system; the corresponding systems of equations are the shuffle equations.…”

Section: Else Gotomentioning

confidence: 99%

“…The teachability problem for EPN's has been shown to be NP-complete in [3]. A related boundedness problem has been considered in [2].…”

Section: Probtem: Boundedness For Epnsmentioning

confidence: 99%