scholarly journals Finite Automata with Generalized Acceptance Criteria

2001 ◽  
Vol Vol. 4 no. 2 ◽  
Author(s):  
Timo Peichl ◽  
Heribert Vollmer
Keyword(s):  
Finite Automata ◽  
Complexity Class ◽  
Input Word ◽  
Boolean Circuits ◽  
Turing Machines ◽  
Acceptance Criteria ◽  
Chomsky Hierarchy ◽  
Computation Tree ◽  
International Audience ◽  
Bounded Complexity

International audience We examine the power of nondeterministic finite automata with acceptance of an input word defined by a leaf language, i.e., a condition on the sequence of leaves in the automaton's computation tree. We study leaf languages either taken from one of the classes of the Chomsky hierarchy, or taken from a time- or space-bounded complexity class. We contrast the obtained results with those known for leaf languages for Turing machines and Boolean circuits.

EFFICIENT DETECTORS AND CONSTRUCTORS FOR SIMPLE LANGUAGES

1991 ◽  
Vol 02 (03) ◽  
pp. 183-205 ◽  
Author(s):  
Dung T. Huynh
Keyword(s):  
Finite Automata ◽  
Boolean Circuits ◽  
Turing Machines ◽  
Constant Depth ◽  
Pushdown Automaton ◽  
Polynomial Size ◽  
Regular Sets ◽  
Context Free ◽  
Pushdown Automata ◽  
Nondeterministic Logspace

In this paper, we investigate the complexity of computing the detector, constructor and lexicographic constructor functions for a given language. The following classes of languages will be considered: (1) context-free languages, (2) regular sets, (3) languages accepted by one-way nondeterministic auxiliary pushdown automata, (4) languages accepted by one-way nondeterministic logspace-bounded Turing machines, (5) two-way deterministic pushdown automaton languages, (6) languages accepted by uniform families of constant-depth polynomial-size Boolean circuits, and (7) languages accepted by multihead finite automata. We show that for the classes (1)–(4), efficient detectors, constructors and lexicographic constructors exist, whereas for (5)– (7) polynomial-time computable detectors, constructors and lexicographic constructors exist iff there are no sparse sets in NP−P (or equivalently, E=NE). Our results provide sharp boundaries between classes of languages which have efficient detectors, constructors and classes of languages for which efficient detectors and constructors do not appear to exist.

ALTERNATING TURING MACHINES WITH MODIFIED ACCEPTING STRUCTURE

1991 ◽  
Vol 02 (04) ◽  
pp. 401-417
Author(s):  
KATSUSHI INOUE ◽  
AKIRA ITO ◽  
ITSUO TAKANAMI
Keyword(s):  
Turing Machine ◽  
Input Word ◽  
Turing Machines ◽  
Closure Properties ◽  
Infinite Hierarchy ◽  
Computation Tree ◽  
On Line ◽  
Alternating Turing Machines

We introduce an alternating Turing machine with modified accepting structure (denoted by MATM), which is an alternating Turing machine whose accepting condition differs from that of an ordinary alternating Turing machine (denoted by ATM). An MATM has a set of accepting state sets rather than a set of accepting states. An input word x is accepted by an MATM M if there is a computation tree of M on x such that the set of states associated with the leaves of the tree is equal to an accepting state set. Let UTM (MUTM) denote an ATM (MATM) with no existential state. We first investigate a relationship between ATM’s and MATM’s, and show that (i) for any function L(n), L(n) space bounded on-line (off-line) ATM’s are equivalent to L(n) space bounded on-line (off-line) MATM’s, and (ii) for any L(n) such that L(n)≥ log log n and limn→∞L(n)/n=0, L(n) space bounded on-line MUTM’s are more powerful than L(n) space bounded on-line UTM’s. We then investigate a relationship between online and off-line, and show for example that for any L(n) such that L(n)≥ log n and limn→∞L(n)/n=0, L(n) space bounded off-line MUTM’s are more powerful than L(n) space bounded on-line MUTM’s. We next show that there exists an infinite hierarchy among accepting powers of L(n) space bounded on-line (off-line) MATM’s and MUTM’s with L(n)≥ log log n and limn→∞L(n)/n=0. Finally, we investigate closure properties of space bounded on-line (off-line) MATM’s and MUTM’s.

One-Way Jumping Finite Automata

2016 ◽  
Vol 27 (03) ◽  
pp. 391-405 ◽  
Author(s):  
Hiroyuki Chigahara ◽  
Szilárd Zsolt Fazekas ◽  
Akihiro Yamamura
Keyword(s):  
Finite Automaton ◽  
Finite Automata ◽  
Input Word ◽  
Chomsky Hierarchy ◽  
Current State ◽  
Language Classes ◽  
Pumping Lemma ◽  
The One ◽  
Classical Language ◽  
Separation Results

We propose the one-way jumping finite automaton model, restricting the jumping relation of the recently introduced jumping finite automaton so that the machine can only jump over symbols it cannot process in its current state. The reading head of a one-way jumping finite automaton moves deterministically in one direction within the input word, whereas movement of the reading head of jumping finite automaton is non-deterministic. The class of languages accepted by one-way jumping finite automata is different from that of jumping finite automata, in particular, it includes all regular languages, as opposed to the latter. We study one-way jumping finite automata and obtain closure properties, a pumping lemma, and separation results with respect to the classical language classes of the Chomsky hierarchy.

HYBRID EXTENDED FINITE AUTOMATA

2007 ◽  
Vol 18 (04) ◽  
pp. 745-760 ◽  
Author(s):  
HENNING BORDIHN ◽  
MARKUS HOLZER ◽  
MARTIN KUTRIB
Keyword(s):  
Finite Automata ◽  
Input Word ◽  
Finite State Automata ◽  
Computational Power ◽  
Chomsky Hierarchy ◽  
Current State ◽  
Different Types ◽  
Finite State ◽  
Finite Set

Extended finite automata are finite state automata equipped with the additional ability to apply an operation on the currently remaining input word, depending on the current state. Hybrid extended finite automata can choose from a finite set of such operations. In this paper, five word operations are taken into consideration which always yield letter-equivalent results, namely reversal and shift operations. The computational power of those machines is investigated, locating the corresponding families of languages in the Chomsky hierarchy. Furthermore, different types of hybrid extended finite automata, defined by the set of operations they are allowed to apply, are compared with each other, demonstrating that there exist dependencies and independencies between the input manipulating operations.

Logical Characterizations of Bounded Query Classes I: Logspace Oracle Machines

1993 ◽  
Vol 18 (1) ◽  
pp. 65-92
Author(s):  
Iain A. Stewart
Keyword(s):  
Truth Table ◽  
Complexity Class ◽  
Polynomial Hierarchy ◽  
Complexity Classes ◽  
Turing Machines ◽  
Complete Problems

We consider three sub-logics of the logic (±HP)*[FOs] and show that these sub-logics capture the complexity classes obtained by considering logspace deterministic oracle Turing machines with oracles in NP where the number of oracle calls is unrestricted and constant, respectively; that is, the classes LNP and LNP[O(1)]. We conclude that if certain logics are of the same expressibility then the Polynomial Hierarchy collapses. We also exhibit some new complete problems for the complexity class LNP via projection translations (the first to be discovered: projection translations are extremely weak logical reductions between problems) and characterize the complexity class LNP[O(1)] as the closure of NP under a new, extremely strict truth-table reduction (which we introduce in this paper).

TWO TOPICS CONCERNING TWO-DIMENSIONAL AUTOMATA OPERATING IN PARALLEL

1992 ◽  
Vol 06 (02n03) ◽  
pp. 211-225 ◽  
Author(s):  
KATSUSHI INOUE ◽  
ITSUO SAKURAMOTO ◽  
MAKOTO SAKAMOTO ◽  
ITSUO TAKANAMI
Keyword(s):  
Turing Machine ◽  
Finite Automata ◽  
Space Complexity ◽  
Two Dimensional ◽  
Turing Machines ◽  
Small Space ◽  
Bottom Up ◽  
Constructible Function ◽  
Deterministic Turing Machine ◽  
Alternating Turing Machines

This paper deals with two topics concerning two-dimensional automata operating in parallel. We first investigate a relationship between the accepting powers of two-dimensional alternating finite automata (2-AFAs) and nondeterministic bottom-up pyramid cellular acceptors (NUPCAs), and show that Ω ( diameter × log diameter ) time is necessary for NUPCAs to simulate 2-AFAs. We then investigate space complexity of two-dimensional alternating Turing machines (2-ATMs) operating in small space, and show that if L (n) is a two-dimensionally space-constructible function such that lim n → ∞ L (n)/ loglog n > 1 and L (n) ≤ log n, and L′ (n) is a function satisfying L′ (n) =o (L(n)), then there exists a set accepted by some strongly L (n) space-bounded two-dimensional deterministic Turing machine, but not accepted by any weakly L′ (n) space-bounded 2-ATM, and thus there exists a rich space hierarchy for weakly S (n) space-bounded 2-ATMs with loglog n ≤ S (n) ≤ log n.

Preface

1997 ◽  
Vol 11 (07) ◽  
pp. 1023-1024
Author(s):  
Serge Miguet ◽  
Annick Montanvert ◽  
P. S. P. Wang
Keyword(s):  
Finite State Machine ◽  
Finite Automata ◽  
Upper Bounds ◽  
Two Dimensional ◽  
Turing Machines ◽  
Closure Properties ◽  
Working Space ◽  
Finite State ◽  
The Individual ◽  
Alternating Turing Machines

Several nonclosure properties of each class of sets accepted by two-dimensional alternating one-marker automata, alternating one-marker automata with only universal states, nondeterministic one-marker automata, deterministic one-marker automata, alternating finite automata, and alternating finite automata with only universal states are shown. To do this, we first establish the upper bounds of the working space used by "three-way" alternating Turing machines with only universal states to simulate those "four-way" non-storage machines. These bounds provide us a simplified and unified proof method for the whole variants of one-marker and/or alternating finite state machine, without directly analyzing the complex behavior of the individual four-way machine on two-dimensional rectangular input tapes. We also summarize the known closure properties including Boolean closures for all the variants of two-dimensional alternating one-marker automata.

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