One-Way Reversible and Quantum Finite Automata with Advice

We examine the characteristic features of reversible and quantum computations in the presence of supplementary external information, known as advice. In particular, we present a simple, algebraic characterization of languages recognized by one-way reversible finite automata augmented with deterministic advice. With a further elaborate argument, we prove a similar but slightly weaker result for bounded-error one-way quantum finite automata with advice. Immediate applications of those properties lead to containments and separations among various language families when they are assisted by appropriately chosen advice. We further demonstrate the power and limitation of randomized advice and quantum advice when they are given to one-way quantum finite automata.Comment: A4, 10pt, 1 figure, 31 pages. This is a complete version of an extended abstract appeared in the Proceedings of the 6th International Conference on Language and Automata Theory and Applications (LATA 2012), March 5-9, 2012, A Coruna, Spain, Lecture Notes in Computer Science, Springer-Verlag, Vol.7183, pp.526-537, 201

Beyond Generalized Multiplicities: Register Machines over Groups

Register machines are a classic model of computing, often seen as a canonical example of a device manipulating natural numbers. In this paper, we de ne register machines operating on general groups instead. This generalization follows the research direction started in multiple previous works. We study the expressive power of register machines as a function of the underlying groups, as well as of allowed ingredients (zero test, partial blindness, forbidden regions). We put forward a fundamental connection between register machines and vector addition systems. Finally, we show how registers over free groups can be used to store and manipulate strings

The placement of the head that maximizes predictability. An information theoretic approach

The minimization of the length of syntactic dependencies is a well-established principle of word order and the basis of a mathematical theory of word order. Here we complete that theory from the perspective of information theory, adding a competing word order principle: the maximization of predictability of a target element. These two principles are in conflict: to maximize the predictability of the head, the head should appear last, which maximizes the costs with respect to dependency length minimization. The implications of such a broad theoretical framework to understand the optimality, diversity and evolution of the six possible orderings of subject, object and verb are reviewed.Comment: in press in Glottometric