The Complexity of the Emptiness Problem for EOL Systems

1992 ◽  
pp. 167-175 ◽  
Author(s):  
Klaus-Jörn Lange ◽  
Michael Schudy
Keyword(s):  
Emptiness Problem

STATELESS ONE-WAY MULTI-HEAD FINITE AUTOMATA WITH PEBBLES

2014 ◽  
Vol 25 (08) ◽  
pp. 1141-1159 ◽  
Author(s):  
MARTIN KUTRIB ◽  
ANDREAS MALCHER ◽  
MATTHIAS WENDLANDT
Keyword(s):  
Finite Automata ◽  
The Other ◽  
Other Hand ◽  
Emptiness Problem ◽  
The Cost

Stateless variants of deterministic one-way multi-head finite automata with pebbles, that is, automata where the heads can drop, sense, and pick up pebbles, are studied. The relation between heads and pebbles is investigated, and a proper double hierarchy concerning these two resources is obtained. Moreover, it is shown that a conversion of an arbitrary automaton to a stateless automaton can always be achieved at the cost of additional heads and/or pebbles. On the other hand, there are languages where one head cannot be traded for any number of additional pebbles and vice versa. Finally, the emptiness problem and related problems are shown to be undecidable even for the ‘simplest’ model, namely, for stateless one-way finite automata with two heads and one pebble.

PUZZLE GRAMMARS AND CONTEXT-FREE ARRAY GRAMMARS

1991 ◽  
Vol 05 (05) ◽  
pp. 663-676 ◽  
Author(s):  
M. NIVAT ◽  
A. SAOUDI ◽  
K. G. SUBRAMANIAN ◽  
R. SIROMONEY ◽  
V. R. DARE
Keyword(s):  
Membership Problem ◽  
Generative Power ◽  
New Model ◽  
Regular Control ◽  
Emptiness Problem ◽  
Np Complete ◽  
Context Free ◽  
Rewriting Rules

We introduce a new model for generating finite, digitized, connected pictures called puzzle grammars and study its generative power by comparison with array grammars. We note how this model generalizes the classical Chomskian grammars and study the effect of direction-independent rewriting rules. We prove that regular control does not increase the power of basic puzzle grammars. We show that for basic and context-free puzzle grammars, the membership problem is NP-complete and the emptiness problem is undecidable.

scholarly journals On stateless multihead automata: Hierarchies and the emptiness problem

2010 ◽  
Vol 411 (3) ◽  
pp. 581-593 ◽  
Author(s):  
Oscar H. Ibarra ◽  
Juhani Karhumäki ◽  
Alexander Okhotin
Keyword(s):  
Emptiness Problem

Emptiness of Ordered Multi-Pushdown Automata is 2ETIME-Complete

2017 ◽  
Vol 28 (08) ◽  
pp. 945-975 ◽  
Author(s):  
Mohamed Faouzi Atig ◽  
Benedikt Bollig ◽  
Peter Habermehl
Keyword(s):  
Lower Bound ◽  
Turing Machine ◽  
Linear Ordering ◽  
Emptiness Problem ◽  
Pushdown Automata ◽  
Exponential Space

We consider ordered multi-pushdown automata, a multi-stack extension of pushdown automata that comes with a constraint on stack operations: a pop can only be performed on the first non-empty stack (which implies that we assume a linear ordering on the collection of stacks). We show that the emptiness problem for multi-pushdown automata is 2ETIME-complete. Containment in 2ETIME is shown by translating an automaton into a grammar for which we can check if the generated language is empty. The lower bound is established by simulating the behavior of an alternating Turing machine working in exponential space. We also compare ordered multi-pushdown automata with the model of bounded-phase (visibly) multi-stack pushdown automata, which do not impose an ordering on stacks, but restrict the number of alternations of pop operations on different stacks.

scholarly journals A classification of intersection type systems

2002 ◽  
Vol 67 (1) ◽  
pp. 353-368
Author(s):  
M. W. Bunder
Keyword(s):  
Type Systems ◽  
Equivalence Classes ◽  
Type Assignment ◽  
Emptiness Problem ◽  
Intersection Types

AbstractThe first system of intersection types. Coppo and Dezani [3], extended simple types to include intersections and added intersection introduction and elimination rules ((ΛI ) and (ΛE) ) to the type assignment system. The major advantage of these new types was that they were invariant under β-equality, later work by Barendregt, Coppo and Dezani [1], extended this to include an (η) rule which gave types invariant under βη-reduction.Urzyczyn proved in [6] that for both these systems it is undecidable whether a given intersection type is empty. Kurata and Takahashi however have shown in [5] that this emptiness problem is decidable for the sytem including (η). but without (ΛI).The aim of this paper is to classify intersection type systems lacking some of (ΛI), (ΛE) and (η), into equivalence classes according to their strength in typing λ-terms and also according to their strength in possessing inhabitants.This classification is used in a later paper to extend the above (un)decidability results to two of the five inhabitation-equivalence classes. This later paper also shows that the systems in two more of these classes have decidable inhabitation problems and develops algorithms to find such inhabitants.

The complexity of weakly recognizing morphisms

2018 ◽  
Vol 53 (1-2) ◽  
pp. 1-17
Author(s):  
Lukas Fleischer ◽  
Manfred Kufleitner
Keyword(s):  
Computational Complexity ◽  
Regular Languages ◽  
Decision Problems ◽  
Membership Problem ◽  
Surjective Morphism ◽  
Infinite Words ◽  
Descriptional Complexity ◽  
Emptiness Problem ◽  
Free Semigroups ◽  
Büchi Automaton

Weakly recognizing morphisms from free semigroups onto finite semigroups are a classical way for defining the class of ω-regular languages, i.e., a set of infinite words is weakly recognizable by such a morphism if and only if it is accepted by some Büchi automaton. We study the descriptional complexity of various constructions and the computational complexity of various decision problems for weakly recognizing morphisms. The constructions we consider are the conversion from and to Büchi automata, the conversion into strongly recognizing morphisms, as well as complementation. We also show that the fixed membership problem is NC1-complete, the general membership problem is in L and that the inclusion, equivalence and universality problems are NL-complete. The emptiness problem is shown to be NL-complete if the input is given as a non-surjective morphism.

Classes of Transfinite Sequences Accepted by Nondeterministic Finite Automata

1984 ◽  
Vol 7 (2) ◽  
pp. 191-223
Author(s):  
Jerzy Wojciechowski
Keyword(s):  
Finite Automaton ◽  
Finite Automata ◽  
Basic Properties ◽  
Nondeterministic Finite Automata ◽  
The Family ◽  
Finite Sequences ◽  
Emptiness Problem ◽  
Nondeterministic Finite Automaton ◽  
Defining Sets

In this paper the notion of a nondeterministic finite automaton acting on arbitrary transfinite sequences is introduced. It is a generalization of the finite automaton on finite sequences and the finite automaton on ω-sequences. The basic properties of the behaviour of such automata are proved. The methods are shown how to construct automata accepting classes A ⋃ B, A ⋂ B, A ∘ B, A*, Aω, A# if we have automata accepting classes A and B. We prove that if a TF-automaton having k states accepts anything then it accepts an α-sequence for a certain, α ∈ { ∑ i = 0 m ω i · a i : ∑ i = 1 m i · a i + a 0 ⩽ k }. Using the foregoing fact, we show that the family of classes definable by TF-automata is not closed with respect to the complement operation, that nondeterministic automata are not equivalent to the deterministic ones and that the emptiness problem for TP-automata is decidable. In the last section we show the construction of TP-automata defining sets {∗α} for α < ω ω and having as few states as possible.

SYSTOLIC TREE WITH BASE AUTOMATA

1991 ◽  
Vol 02 (03) ◽  
pp. 221-236 ◽  
Author(s):  
A. MONTI ◽  
D. PARENTE
Keyword(s):  
Sufficient Condition ◽  
Tree Automata ◽  
Necessary And Sufficient Condition ◽  
The Family ◽  
Emptiness Problem ◽  
Necessary And Sufficient ◽  
Natural Way

Different systolic tree automata (STA) with base (T(b)−STA) are compared. This is a subclass of STA with interesting properties of modularity. We give a necessary and sufficient condition for the inclusion between classes of languages accepted by T(b)− STA, (L(T(b)−STA)), as b varies. We focus on T(b)−STA obtained by varying the base b in a natural way. We prove that for every base b within this framework there exists an a such that L(T(a)−STA) is not contained in L(T(b)−STA). We characterize the family of languages accepted by T(b)−STA when the input conditions are relaxed. Moreover we show that the emptiness problem is decidable for T(b)−STA.

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