Two-tape finite automata with quantum and classical states

{\it Two-way finite automata with quantum and classical states} (2QCFA) were introduced by Ambainis and Watrous, and {\it two-way two-tape deterministic finite automata} (2TFA) were introduced by Rabin and Scott. In this paper we study 2TFA and propose a new computing model called {\it two-way two-tape finite automata with quantum and classical states} (2TQCFA). First, we give efficient 2TFA algorithms for recognizing languages which can be recognized by 2QCFA. Second, we give efficient 2TQCFA algorithms to recognize several languages whose status vis-a-vis 2QCFA have been posed as open questions, such as $L_{square}=\{a^{n}b^{n^{2}}\mid n\in \mathbf{N}\}$. Third, we show that $\{a^{n}b^{n^{k}}\mid n\in \mathbf{N}\}$ can be recognized by {\it $(k+1)$-tape deterministic finite automata} ($(k+1)$TFA). Finally, we introduce {\it $k$-tape automata with quantum and classical states} ($k$TQCFA) and prove that $\{a^{n}b^{n^{k}}\mid n\in \mathbf{N}\}$ can be recognized by $k$TQCFA.Comment: 25 page

Bilevel optimization approach to design of network of bike lanes

A bike lane is an effective way to improve cycling safety and to decrease greenhouse gas emissions with the promotion of cycling. Improvements include high-quality off-road facilities and on-road bike lanes. Whereas construction of off-road lanes is not always possible because of urban land constraints and construction costs, on-road lanes can be a cost-effective alternative. An optimization framework for the design of a network of bike lanes in an urban road network was proposed. This framework identified links on which a bike lane could be introduced. Allocation of a lane to cyclists would increase the use of cycling, although it could disadvantage auto traffic. The presented approach balances the effects of a bike lane for all stakeholders. A bilevel optimization was proposed to encompass the benefits of cyclists and car users at the upper level and a model for traffic and bike demand assignment at the lower level. The objective function was defined by a weighted sum of a measure for private car users (total travel time) versus a measure for bike users (total travel distance on bike lanes). A genetic algorithm was developed to solve the bilevel formulation, which included introduction of a special crossover technique and a mutation technique. The proposed optimization will help transport authorities at the planning stage to quantify the outcomes of various strategies for active transport

A Satisfiability-based Approach for Embedding Generalized Tanglegrams on Level Graphs

A tanglegram is a pair of trees on the same set of leaves with matching leaves in the two trees joined by an edge. Tanglegrams are widely used in computational biology to compare evolutionary histories of species. In this paper we present a formulation of two related combinatorial embedding problems concerning tanglegrams in terms of CNF-formulas. The first problem is known as planar embedding and the second as crossing minimization problem. We show that our satisfiability formulation of these problems can handle a much more general case with more than two, not necessarily binary or complete, trees defined on arbitrary sets of leaves and allowed to vary their layouts

Descriptional Complexity of Bounded Context-Free Languages

Finite-turn pushdown automata (PDA) are investigated concerning their descriptional complexity. It is known that they accept exactly the class of ultralinear context-free languages. Furthermore, the increase in size when converting arbitrary PDAs accepting ultralinear languages to finite-turn PDAs cannot be bounded by any recursive function. The latter phenomenon is known as non-recursive trade-off. In this paper, finite-turn PDAs accepting letter-bounded languages are considered. It turns out that in this case the non-recursive trade-off is reduced to a recursive trade-off, more precisely, to an exponential trade-off. A conversion algorithm is presented and the optimality of the construction is shown by proving tight lower bounds. Furthermore, the question of reducing the number of turns of a given finite-turn PDA is studied. Again, a conversion algorithm is provided which shows that in this case the trade-off is at most polynomial

Cooperating Physical Robots: A Lesson in Playing Robotic Soccer

Having a robot that carries out a task for you is certainly of some help. Having a group of robots seems to be even better because in this case the task may be finished faster and more reliably. However, dealing with a group of robots can make some problems more difficult. In this paper we sketch some of the advantages and some problems that come up when dealing with groups of robots. In particular, we describe techniques as they have been developed and tested in the area of robotic soccer

GRENADA - POLITICS, ECONOMICS AND SOCIETY - THORNDIKE,T

We present quantum algorithms for the following graph problems: finding a maximal bipartite matching in time O(n sqrt{m+n} log n), finding a maximal non-bipartite matching in time O(n^2 (sqrt{m/n} + log n) log n), and finding a maximal flow in an integer network in time O(min(n^{7/6} sqrt m * U^{1/3}, sqrt{n U} m) log n), where n is the number of vertices, m is the number of edges, and U <= n^{1/4} is an upper bound on the capacity of an edge.Comment: 13 pages, v2: added an Omega(n^2) lower bound for network flow