# From Regular to Strictly Locally Testable Languages

@article{CrespiReghizzi2012FromRT, title={From Regular to Strictly Locally Testable Languages}, author={Stefano Crespi-Reghizzi and Pierluigi San Pietro}, journal={Int. J. Found. Comput. Sci.}, year={2012}, volume={23}, pages={1711-1728} }

A classical result (often credited to Y. Medvedev) states that every language recognized by a finite automaton is the homomorphic image of a local language, over a much larger so-called local alphabet, namely the alphabet of the edges of the transition graph. Local languages are characterized by the value k = 2 of the sliding window width in the McNaughton and Papert's infinite hierarchy of strictly locally testable languages (k-slt). We generalize Medvedev's result in a new direction, studying…

## 11 Citations

### Regular Languages as Local Functions with Small Alphabets

- Computer ScienceCAI
- 2019

By encoding the automaton computations using comma-free codes, it is proved that any regular language is the image computed by a length-preserving local function, which is defined on an alphabet that extends the terminal alphabet by just one additional letter.

### Strict Local Testability with Consensus Equals Regularity

- Computer ScienceCIAA
- 2012

Using a recent generalization of Medvedev's homomorphic characterization of regular languages, it is proved that regular languages are exactly the consensual languages based on strictly locally testable sets, a result that hints at a novel parallel decomposition of finite automata into locallyTestable components.

### Reducing the Local Alphabet Size in Tiling Systems for Picture Languages

- Computer Science
- 2021

This result lifts into 2D a known similar property of regular word languages, concerning the minimal alphabetic ratio needed to deﬁne a language by means of a projection of an SLT word language, using 2D comma-free codes, which have the property of synchronizability.

### Reducing the local alphabet size in tiling systems by means of 2D comma-free codes

- Computer ScienceTheor. Comput. Sci.
- 2022

The result reproduces in two dimensions a similar property (known as Extended Medvedev’s theorem) of the regular word languages, concerning the minimal alphabetic ratio needed to define a language by means of a projection of an SLT word language.

### Strict Local Testability with Consensus Equals Regularity, and Other Properties

- Computer ScienceInt. J. Found. Comput. Sci.
- 2013

It is shown that all and only the regular languages are consensually generated by a strictly locally testable base; the result is based on a generalization of Medvedev's homomorphic characterization of regular languages.

### The Missing Case in Chomsky-Schützenberger Theorem

- Computer ScienceLATA
- 2016

A new non-erasing variant of CST is presented that uses a Dyck alphabet independent from the grammar size and a regular language that is strictly-locally-testable, similarly to a recent generalization of Medvedev theorem for regular languages.

### Implementation and Application of Automata

- Computer ScienceLecture Notes in Computer Science
- 2012

It is proved that the state complexity bounds that hold for arbitrary regular languages are also met by the languages Un(a, b, c) for union, intersection, difference, symmetric difference, product (concatenation) and star.

### Consensual languages: a simple parallel machine model

- Computer Science
- 2014

It is shown that regular languages coincide with the consensual languages b ased on strictly locally testable computations, and a method for designing consensual languages so that t heir union is consensual is shown.

### Non-erasing Chomsky-Sch{ü}tzenberger theorem with grammar-independent alphabet

- Computer ScienceInf. Comput.
- 2019

### On the Generative Capacity of Contextual Grammars with Strictly Locally Testable Selection Languages

- Linguistics, Computer ScienceNCMA
- 2022

This work investigates contextual grammars with strictly locally testable selection languages and compares those families to families which are based on monoidal, nilpotent, combinational, deﬁnite, suf ﬁx-closed, ordered, commutative, circular, non-counting, power-separating, or union-free languages.

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