Finite automata with advice tapes

We define a model of advised computation by finite automata where the advice is provided on a separate tape. We consider several variants of the model where the advice is deterministic or randomized, the input tape head is allowed real-time, one-way, or two-way access, and the automaton is classical or quantum. We prove several separation results among these variants, demonstrate an infinite hierarchy of language classes recognized by automata with increasing advice lengths, and establish the relationships between this and the previously studied ways of providing advice to finite automata.Comment: Corrected typo

Inkdots as advice for finite automata

We examine inkdots placed on the input string as a way of providing advice to finite automata, and establish the relations between this model and the previously studied models of advised finite automata. The existence of an infinite hierarchy of classes of languages that can be recognized with the help of increasing numbers of inkdots as advice is shown. The effects of different forms of advice on the succinctness of the advised machines are examined. We also study randomly placed inkdots as advice to probabilistic finite automata, and demonstrate the superiority of this model over its deterministic version. Even very slowly growing amounts of space can become a resource of meaningful use if the underlying advised model is extended with access to secondary memory, while it is famously known that such small amounts of space are not useful for unadvised one-way Turing machines.Comment: 14 page

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

Quantum Branching Programs and Space-Bounded Nonuniform Quantum Complexity

In this paper, the space complexity of nonuniform quantum computations is investigated. The model chosen for this are quantum branching programs, which provide a graphic description of sequential quantum algorithms. In the first part of the paper, simulations between quantum branching programs and nonuniform quantum Turing machines are presented which allow to transfer lower and upper bound results between the two models. In the second part of the paper, different variants of quantum OBDDs are compared with their deterministic and randomized counterparts. In the third part, quantum branching programs are considered where the performed unitary operation may depend on the result of a previous measurement. For this model a simulation of randomized OBDDs and exponential lower bounds are presented.Comment: 45 pages, 3 Postscript figures. Proofs rearranged, typos correcte

Reactive Turing Machines

We propose reactive Turing machines (RTMs), extending classical Turing machines with a process-theoretical notion of interaction, and use it to define a notion of executable transition system. We show that every computable transition system with a bounded branching degree is simulated modulo divergence-preserving branching bisimilarity by an RTM, and that every effective transition system is simulated modulo the variant of branching bisimilarity that does not require divergence preservation. We conclude from these results that the parallel composition of (communicating) RTMs can be simulated by a single RTM. We prove that there exist universal RTMs modulo branching bisimilarity, but these essentially employ divergence to be able to simulate an RTM of arbitrary branching degree. We also prove that modulo divergence-preserving branching bisimilarity there are RTMs that are universal up to their own branching degree. Finally, we establish a correspondence between executability and finite definability in a simple process calculus