Multi-Head Finite Automata: Characterizations, Concepts and Open Problems

  title={Multi-Head Finite Automata: Characterizations, Concepts and Open Problems},
  author={Markus Holzer and Martin Kutrib and Andreas Malcher},
Multi-head finite automata were introduced in (Rabin, 1964) and (Rosenberg, 1966). Since that time, a vast literature on computational and descriptional complexity issues on multi-head finite automata documenting the importance of these devices has been developed. Although multi-head finite automata are a simple concept, their computational behavior can be already very complex and leads to undecidable or even non-semi-decidable problems on these devices such as, for example, emptiness… 

Asynchronous Multi-Tape Automata Intersection: Undecidability and Approximation

This paper investigates to what extent it is still feasible to use multi-tape automata as recognizer of polyadic predicates on words, and presents an algorithm that computes under-approximations of the intersection.

What's Decidable About Asynchronous Multi-Tape Automata?

It is proved that determining whether the intersection of two multi-tape automata A,B is expressible as an automaton is neither decidable nor semi-decidable; and that closure under intersection with equality is tantamount to the simpler class of synchronous automata.

A Simulation of Oblivious Multi-head One-way Finite Automata by Real-time Cellular Automata

The simulation of a simple, yet significantly powerful, sequential model by cellular automata called oblivious multi-head one-way finite automata, characterized by having its heads moving only forward, on a trajectory that only depends on the length of the input.

A speed-up of oblivious multi-head finite automata by cellular automata

A parallel speed-up of a simple, yet significantly powerful, sequential model by cellular automata is presented, called oblivious multi-head finite automata and is characterized by the fact that the trajectory of the heads only depends on the length of the input word.

On the Hierarchy Classes of Finite Ultrametric Automata

It is proved that in the one-way setting there is a language that can be recognized by a one-head ultrametric finite automaton and cannot be recognizing by any k-head non-deterministic finite automata.

Reversible Multi-head Finite Automata Characterize Reversible Logarithmic Space

This work exhibits a clean RMFA simulation of logarithmic space reversible Turing machines, and proves that reversible and deterministic multi-head finite automata recognize the same languages.

Structural complexity of multi-valued partial functions computed by nondeterministic pushdown automata

This paper extensively discuss containments, separations, and refinements among various classes of functions obtained from the CFL functions by applying Boolean operations, functional composition, many-one relativization, and Turing relatvization.

UNIVERSIDADE ESTADUAL DE CAMPINAS On the Quantum-Classical Separation of Marking and Multi-Head Automata

This work proposes a new general marking automaton based on the 2QCFA model and proves that this model is more powerful than its classical analogues in terms of computability and complexity.

On the power of two-way multihead quantum finite automata

It has been proved that a language which cannot be recognizing by any one-way and multi-letter quantum finite automata can be recognized by two-way quantum finite Automata with two heads and it has been investigated that quantum variant of two- way deterministic multihead finite automaton takes less number of heads to recognize a language containing of all words whose length is a prime number.

Ultrametric Automata with One Head Versus Multihead Nondeterministic Automata

Advantages of ultrametric automata with one head versus multihead deterministic and nondeterministic automata are observed.



On multi-head finite automata

The relationships among the multi-head languages and the context-free and context-sensitive languages are investigated, and the adage, "Two heads are better than one," is generalized.

On stateless multihead automata: Hierarchies and the emptiness problem

Nondeterminism and the size of two way finite automata

This work considers two questions on regular languages resembling these open problems of P, NP, and LOGSPACE, and 2-way non-deterministic and2-way deterministic finite automata.

On partially blind multihead finite automata

On the descriptional power of heads, counters, and pebbles

Descriptional complexity of bounded context-free languages

Finite-turn pushdown automata accepting letter-bounded languages are considered and it turns out that in this case the non-recursive trade-off is reduced to a recursive trade-offs, more precisely, to an exponentialTrade-off.

Bounded-Reversal Multihead Finite Automata Languages

On the Computational Capacity of Parallel Communicating Finite Automata

It is shown that deterministic returning and non-returning devices are equivalent, and that there are languages which are accepted by deterministic return and centralized systems but cannot be accepted by Deterministic non- returning centralized systems.

Multi-head finite automata: data-independent versus data-dependent computations

  • M. Holzer
  • Computer Science
    Theor. Comput. Sci.
  • 2002

Finite Automata and Their Decision Problems

Finite automata are considered as instruments for classifying finite tapes as well as generalizations of the notion of an automaton are introduced and their relation to the classical automata is determined.