Most Complex Non-Returning Regular Languages

A regular language $L$ is non-returning if in the minimal deterministic finite automaton accepting it there are no transitions into the initial state. Eom, Han and Jir\'askov\'a derived upper bounds on the state complexity of boolean operations and Kleene star, and proved that these bounds are tight using two different binary witnesses. They derived upper bounds for concatenation and reversal using three different ternary witnesses. These five witnesses use a total of six different transformations. We show that for each $n\ge 4$ there exists a ternary witness of state complexity $n$ that meets the bound for reversal and that at least three letters are needed to meet this bound. Moreover, the restrictions of this witness to binary alphabets meet the bounds for product, star, and boolean operations. We also derive tight upper bounds on the state complexity of binary operations that take arguments with different alphabets. We prove that the maximal syntactic semigroup of a non-returning language has $(n-1)^n$ elements and requires at least $\binom{n}{2}$ generators. We find the maximal state complexities of atoms of non-returning languages. Finally, we show that there exists a most complex non-returning language that meets the bounds for all these complexity measures.Comment: 22 pages, 6 figure

On some remarkable operads constructed from Baxter operators

Language theory, symbolic dynamics, modelisation of viral insertion into the genetic code of a host cell motivate the introduction of new types of bialgebras whose coalgebra parts are not necessarily coassociative. One of the aim of this article is to study what type of (associative) algebras (and thus binary quadratic and non-symmetric operads) appear when such or such coalgebraic structures are used to decribe for instance combinatorial objects such as weighted directed graphs, trees, substitutions and so forth.Comment: 45 pages, 4 figure

She inches glass to break: conversations between friends

She inches glass to break: conversations between friends is a project that aims to manifest, through research and practice, my own feminist language within the videos I have produced in my final year of my Masters of Fine Arts. My feminist language is Australian and intersectional, invested in combating sexism, racism and in deepening language and representation around sexuality in relation to Asian women. This project discusses my video She inches glass to break (2018) in length, which created intersectional feminist dialogue in response to feminist filmmaker Ulrike Ottinger’s film Ticket of No Return (1979) and Breakfast at Tiffany’s (1961). Additionally, given this project’s investment in language, this body of work is influenced both by aspects of psychoanalysis – in which speech is central to a “therapeutic action” – and by feminist linguistics in which linguistic analysis reveals some of the mechanisms through which language constrains, coerces and represents women, men and non-binary people in oppressive ways

Bilingualism and Communicative Benefits

We examine patterns of acquiring non-native languages in a model with two languages and two populations with heterogeneous learning skills, where every individual faces a binary choice of learning the foreign language or refraining from doing so. We show that both interior and corner linguistic equilibria can emerge in our framework, and that the fraction of learners of the foreign language is higher in the country with a higher gross cost adjusted communicative benefit. It turns out that this observation is consistent with the data on language proficiency in bilingual countries such as Belgium and Canada. We also point out that linguistic equilibria can exhibit insufficient learning which opens the door for government policies that are beneficial for both populations.Communicative Benefits, Linguistic Equilibrium, Learning Costs

A non-interleaving process calculus for multi-party synchronisation

We introduce the wire calculus. Its dynamic features are inspired by Milner's CCS: a unary prefix operation, binary choice and a standard recursion construct. Instead of an interleaving parallel composition operator there are operators for synchronisation along a common boundary and non-communicating parallel composition. The (operational) semantics is a labelled transition system obtained with SOS rules. Bisimilarity is a congruence with respect to the operators of the language. Quotienting terms by bisimilarity results in a compact closed category

Symmetric Groups and Quotient Complexity of Boolean Operations

The quotient complexity of a regular language L is the number of left quotients of L, which is the same as the state complexity of L. Suppose that L and L' are binary regular languages with quotient complexities m and n, and that the transition semigroups of the minimal deterministic automata accepting L and L' are the symmetric groups S_m and S_n of degrees m and n, respectively. Denote by o any binary boolean operation that is not a constant and not a function of one argument only. For m,n >= 2 with (m,n) not in {(2,2),(3,4),(4,3),(4,4)} we prove that the quotient complexity of LoL' is mn if and only either (a) m is not equal to n or (b) m=n and the bases (ordered pairs of generators) of S_m and S_n are not conjugate. For (m,n)\in {(2,2),(3,4),(4,3),(4,4)} we give examples to show that this need not hold. In proving these results we generalize the notion of uniform minimality to direct products of automata. We also establish a non-trivial connection between complexity of boolean operations and group theory