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

@inproceedings{Holzer2008MultiHeadFA, title={Multi-Head Finite Automata: Characterizations, Concepts and Open Problems}, author={Markus Holzer and Martin Kutrib and Andreas Malcher}, booktitle={CSP}, year={2008} }

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…

## 29 Citations

### Asynchronous Multi-Tape Automata Intersection: Undecidability and Approximation

- Computer Science
- 2012

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?

- Computer Science
- 2012

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

- Computer ScienceJAC
- 2010

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

- Computer ScienceSTACS
- 2011

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

- Computer ScienceSOFSEM
- 2015

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

- Computer ScienceLATA
- 2012

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

- Computer ScienceICTCS
- 2014

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

- Computer Science
- 2014

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

- Computer ScienceRAIRO Theor. Informatics Appl.
- 2019

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

- Computer ScienceSOFSEM
- 2015

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

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