# A Myhill-Nerode theorem for automata with advice

@inproceedings{Kruckman2012AMT, title={A Myhill-Nerode theorem for automata with advice}, author={Alex Kruckman and Sasha Rubin and John Sheridan and Ben Zax}, booktitle={International Symposium on Games, Automata, Logics and Formal Verification}, year={2012} }

An automaton with advice is a finite state automaton which has access to an additional fixed infinite string called an advice tape. We refine the Myhill-Nerode theorem to characterize the languages of finite strings that are accepted by automata with advice. We do the same for tree automata with advice.

## 7 Citations

### Advice Automatic Structures and Uniformly Automatic Classes

- Mathematics, Computer ScienceCSL
- 2017

It is proved that the class of all torsion-free Abelian groups of rank one is uniformly omega-automatic and that there is a uniform omega-tree-automatic presentation of the classof all Abelian Groups up to elementary equivalence and of theclass of all countable divisible Abelian Group groups.

### On the Complexity of Infinite Advice Strings

- Computer ScienceICALP
- 2018

The main results explore the connections between classes of advice automatic structures, MSO-transductions and two-way transducers and suggest a closer study of the resulting hierarchy over infinite words.

### Comparing the power of advice strings: a notion of complexity for infinite words

- Computer ScienceArXiv
- 2018

The main results explore the connections between classes of advice automatic structures, MSO-transductions and two-way transducers and suggest a closer study of the resulting hierarchy over infinite words.

### Monadic Second-Order Logic with Arbitrary Monadic Predicates

- Mathematics, Computer ScienceMFCS
- 2014

We study Monadic Second-Order Logic (MSO) over finite words, extended with (non-uniform arbitrary) monadic predicates. We show that it defines a class of languages that has algebraic,…

### Algorithmic Solutions via Model Theoretic Interpretations

- Computer Science, Mathematics
- 2017

This dissertation introduces automatic presentations with advice for several automata models, which are closely related to monadic second-order interpretations over set variables, and investigates the efficiency of this approach by analysing the runtime of the generic automata-based model checking algorithm in terms of the complexity of the given presentation.

### Automatic Structures: Twenty Years Later

- Computer ScienceLICS
- 2020

This tutorial presents an introduction into the history and basic definitions of automatic structures, and surveys the achievements in the study of different variants ofautomatic structures.

### On the Width of Regular Classes of Finite Structures

- Mathematics, Computer ScienceCADE
- 2019

It is shown that the problem of counting satisfying assignments for a first-order logic formula in a structure of constant width is fixed parameter tractable when parameterized by the width parameter and can be solved in quadratic time with respect to the length of the input representation of the structure.

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