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LOCAL TESTABILITY Un concetto ricco di suggestioni e un dialogo a distanza con Stefano.

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Presentation on theme: "LOCAL TESTABILITY Un concetto ricco di suggestioni e un dialogo a distanza con Stefano."— Presentation transcript:

1 LOCAL TESTABILITY Un concetto ricco di suggestioni e un dialogo a distanza con Stefano

2 LT appare in svariati contesti Medvedev theorem Comsky-Schutzenberger theorem Linguistics Learning models and inductive inference DNA and Splicing Systems Brain models for language recognition Systems of finite type in Symbolic Dynamics Recognizable 2D-languages Aural pattern recognition capabilities in humans and animals Theory of semigroups etc.

3 Un testo fondamentale Robert McNaughton and Seymour Papert COUNTER-FREE AUTOMATA The MIT Press, 1971 Sviluppa la teoria matematica di Non-Counting Property Local Testability

4 Negli anni 70 S. Crespi-Reghizzi Non-Counting languages and learning Proc.Nato Adv. Study on Computer Learning Processes, 1974 S. Crespi-Reghizzi, G. Guida, D. Mandrioli, Non-counting context- free languages, J. ACM 25, 1978 A. Restivo Codes and aperiodic languages LNCS 2, 1973 A. Restivo On a question of McNaughton and Papert Information and Control 25, 1974

5 Two-Dimensional Languages Stefano con Matteo Pradella, Alessandra Cherubini Pierluigi San Pietro Tile rewriting grammars Regional Tile grammars A. R. con Dora Giammarresi Finite-State Recognizability by Tiling Systems

6 Altre ricerche ispirate, o con riferimento, a LT Stefano Associative Language descriptions Consensual languages A generalizatio of Medvedev’s theorem A. R. Symbolic Dynamics and Codes Combinatorics of Minimal Forbidden Words

7 Associative Language Descriptions A combination of locally testable and constituent structure models. A.Cherubini, S. Crespi-Reghizzi, P. San Pietro Languages based on structural local testability S. Crespi-Reghizzi, V. Braitenberg Toward a brain compatible theory of syntax based on local testability S. Crespi-Reghizzi, M. Pradella, P. San Pietro Associative definition of programming languages

8 A generalization of Medvedev’s theorem S. Crespi-Reghizzi, P. San Pietro From Regular languages to strictly locally testable languages Investigates the relationship between the width of the sliding window and the alphabetic ratio

9 Consensual Languages A language definition device based on agreemen, or consensus, between similar words S. Crespi-Reghizzi, P. San Pietro Languages defined by consensual computations S. Crespi-Reghizzi, P. San Pietro Strict local testability with consensus equals regularity

10 Stefano, quante altre idee innovative ci proporrai ancora, più o meno ispirate alla Local Testability ?

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