Finite automata models of quantized systems: conceptual status and outlook

Since Edward Moore, finite automata theory has been inspired by physics, in particular by quantum complementarity. We review automaton complementarity, reversible automata and the connections to generalized urn models. Recent developments in quantum information theory may have appropriate formalizations in the automaton context.Comment: 12 pages, prepared for the Sixth International Conference on Developments in Language Theory, Kyoto, Japan, September 18-21, 200

From algebra to logic: there and back again -- the story of a hierarchy

This is an extended survey of the results concerning a hierarchy of languages that is tightly connected with the quantifier alternation hierarchy within the two-variable fragment of first order logic of the linear order.Comment: Developments in Language Theory 2014, Ekaterinburg : Russian Federation (2014

Graph Spectral Properties of Deterministic Finite Automata

We prove that a minimal automaton has a minimal adjacency matrix rank and a minimal adjacency matrix nullity using equitable partition (from graph spectra theory) and Nerode partition (from automata theory). This result naturally introduces the notion of matrix rank into a regular language L, the minimal adjacency matrix rank of a deterministic automaton that recognises L. We then define and focus on rank-one languages: the class of languages for which the rank of minimal automaton is one. We also define the expanded canonical automaton of a rank-one language.Comment: This paper has been accepted at the following conference: 18th International Conference on Developments in Language Theory (DLT 2014), August 26 - 29, 2014, Ekaterinburg, Russi

Computer aided synthesis: a game theoretic approach

In this invited contribution, we propose a comprehensive introduction to game theory applied in computer aided synthesis. In this context, we give some classical results on two-player zero-sum games and then on multi-player non zero-sum games. The simple case of one-player games is strongly related to automata theory on infinite words. All along the article, we focus on general approaches to solve the studied problems, and we provide several illustrative examples as well as intuitions on the proofs.Comment: Invitation contribution for conference "Developments in Language Theory" (DLT 2017

An automata characterisation for multiple context-free languages

We introduce tree stack automata as a new class of automata with storage and identify a restricted form of tree stack automata that recognises exactly the multiple context-free languages.Comment: This is an extended version of a paper with the same title accepted at the 20th International Conference on Developments in Language Theory (DLT 2016

Accommodating multiculturalism and biculturalism in Aotearoa New Zealand: implication for language education.

The field of language education in Aotearoa New Zealand, as elsewhere, has developed significantly since its early and almost exclusive focus on the acquisition of English literacy in schools. As the field has expanded, so too has the range of language education sectors addressed and the theoretical approaches and understandings employed in relation to language and literacy education. Both developments have resulted in a more coordinated literacy education policy - exemplified to date most clearly in the New Zealand Literacy Taskforce - and a more situated, less monolithic understanding of the widely different literacies available to learners. Despite these developments, however, one area still remains noticeably under-theorised and marginalized in relation to the ongoing development of language and literacy education policy in Aotearoa New Zealand - the place of second language learners within it. This paper explores this lacuna and the potential policy implications of addressing and integrating first and second language educational concerns within an evolving national literacy education policy. This has particular implications for the further development of bilingual education - both for Maori and, possibly, other minority groups - and for the related possibilities of multicultural education. It also requires a wider and clearer recognition of minority language education rights, as developed within both international law and political theory, in order to apply these rights appropriately to an Aotearoa New Zealand context which is currently witnessing rapid and extensive demographic (and linguistic) change