28,270 research outputs found

    The Countdown Problem

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    We systematically develop a functional program that solves the countdown problem, a numbers game in which the aim is to construct arithmetic expressions satisfying certain constraints. Starting from a formal specification of the problem, we present a simple but inefficient program that solves the problem, and prove that this program is correct. We then use program fusion to calculate an equivalent but more efficient program, which is then further improved by exploiting arithmetic properties

    Phase transition in the Countdown problem

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    Here we present a combinatorial decision problem, inspired by the celebrated quiz show called the countdown, that involves the computation of a given target number T from a set of k randomly chosen integers along with a set of arithmetic operations. We find that the probability of winning the game evidences a threshold phenomenon that can be understood in the terms of an algorithmic phase transition as a function of the set size k. Numerical simulations show that such probability sharply transitions from zero to one at some critical value of the control parameter, hence separating the algorithm's parameter space in different phases. We also find that the system is maximally efficient close to the critical point. We then derive analytical expressions that match the numerical results for finite size and permit us to extrapolate the behavior in the thermodynamic limit.Comment: Submitted for publicatio

    THE EFFECT OF TRAFFIC LIGHT COUNTDOWN TIMER ON RED LIGHT RUNNING

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    Red-light running occurs when a driver enters an intersection after the traffic signal has turned red. This situation then resolves to minor accidents and even lost of life. Due to this critical problem, countdown timer is installed at the traffic light with a hope to reduce the number of red light violent. However, the effect of this countdown timer to the red light running in Malaysia is never been studied. This project evaluated the case in detail and clarifies the findings. Two intersections are chosen which are with and without countdown timer that representing an upstream and a downstream. Three stations are identified, namely Station 1 (Intersection Balai Polis Pekan Baru), Station 2 (Intersection Silibin) and Station 3 (Intersection Pasir Puteh). Traffic survey is conducted by leaving the video camera at the right angle of the intersection to capture the intersection movements. The recorded data are run through a television to project the visual and traffic count is performed. The levels of service (LOS) of all the intersections involved in the traffic survey are obtained through aaSIDRA software. The percentages of red light running were derived from the data summary. The Chi-Square statistical analysis is carried out from those percentages. The statistical analysis shows that the effect of countdown timer on the number of red light running for Station 1 and Station 2, are not significant but shown a significant effect on Station 3 at 95% confidence level. By percentages, the road users who comply with the red light, cross the intersection during amber and violate the red light are approximately the same for both intersections with and without timer at Station 1. The percentages of road users who violate the red light and cross the intersection during amber were approximately reduced by half at intersection with countdown timer in Station 2. The percentage of compliance to the red light was tremendously higher at the upstream compared downstream intersection in Station 3 case. The percentages of road user who violate the red light and cross the intersection during amber were remarkably lower at intersection with countdown timer. Results obtained showed that the installation of countdown timer at the signalized intersection able to reduce the number of red light running

    Automatic programming of simulation models

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    The concepts of software engineering were used to improve the simulation modeling environment. Emphasis was placed on the application of an element of rapid prototyping, or automatic programming, to assist the modeler define the problem specification. Then, once the problem specification has been defined, an automatic code generator is used to write the simulation code. The following two domains were selected for evaluating the concepts of software engineering for discrete event simulation: manufacturing domain and a spacecraft countdown network sequence. The specific tasks were to: (1) define the software requirements for a graphical user interface to the Automatic Manufacturing Programming System (AMPS) system; (2) develop a graphical user interface for AMPS; and (3) compare the AMPS graphical interface with the AMPS interactive user interface

    A Markovian event-based framework for stochastic spiking neural networks

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    In spiking neural networks, the information is conveyed by the spike times, that depend on the intrinsic dynamics of each neuron, the input they receive and on the connections between neurons. In this article we study the Markovian nature of the sequence of spike times in stochastic neural networks, and in particular the ability to deduce from a spike train the next spike time, and therefore produce a description of the network activity only based on the spike times regardless of the membrane potential process. To study this question in a rigorous manner, we introduce and study an event-based description of networks of noisy integrate-and-fire neurons, i.e. that is based on the computation of the spike times. We show that the firing times of the neurons in the networks constitute a Markov chain, whose transition probability is related to the probability distribution of the interspike interval of the neurons in the network. In the cases where the Markovian model can be developed, the transition probability is explicitly derived in such classical cases of neural networks as the linear integrate-and-fire neuron models with excitatory and inhibitory interactions, for different types of synapses, possibly featuring noisy synaptic integration, transmission delays and absolute and relative refractory period. This covers most of the cases that have been investigated in the event-based description of spiking deterministic neural networks

    Branding the Unbrandable: A Solution to Rebranding the MTA

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    Limit Your Consumption! Finding Bounds in Average-energy Games

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    Energy games are infinite two-player games played in weighted arenas with quantitative objectives that restrict the consumption of a resource modeled by the weights, e.g., a battery that is charged and drained. Typically, upper and/or lower bounds on the battery capacity are part of the problem description. Here, we consider the problem of determining upper bounds on the average accumulated energy or on the capacity while satisfying a given lower bound, i.e., we do not determine whether a given bound is sufficient to meet the specification, but if there exists a sufficient bound to meet it. In the classical setting with positive and negative weights, we show that the problem of determining the existence of a sufficient bound on the long-run average accumulated energy can be solved in doubly-exponential time. Then, we consider recharge games: here, all weights are negative, but there are recharge edges that recharge the energy to some fixed capacity. We show that bounding the long-run average energy in such games is complete for exponential time. Then, we consider the existential version of the problem, which turns out to be solvable in polynomial time: here, we ask whether there is a recharge capacity that allows the system player to win the game. We conclude by studying tradeoffs between the memory needed to implement strategies and the bounds they realize. We give an example showing that memory can be traded for bounds and vice versa. Also, we show that increasing the capacity allows to lower the average accumulated energy.Comment: In Proceedings QAPL'16, arXiv:1610.0769
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