Includes bibliographical references.

String Matching Using Quantum Fourier Transform -- Permutation Entropy of Card Shuffling -- Notes on Language Relations among Transition P Systems -- Synchronization of ad hoc Clock Networks.

[Article Title: String Matching Using Quantum Fourier Transform/ Jeffrey A. Aborot and Henry N. Adorna, p. 1-9]

Abstract: Pattern matching has always been applicable to many areas of interest. Particular to the string data structure, this problem abstracts computational tasks found in areas such as computational biology, signal processing and network security. Due to its high applicability several approaches has al-ready been devised for solving the problem using its various models. Main classical approaches developed are dynamic programming, automata-based algorithms, bit-parallelism techniques and filtering. One particular approach to string matching problem is the semi-numerical approach of viewing pattern matching as the process of multiplying polynomials. A classical tech-nique used for speeding up multiplication is the convolution method which uses Discrete Fourier Transform and its in-verse. The Fast Fourier Transform algorithm can be used to speed up computation of the Discrete Fourier Transform by a large factor. In this paper we propose a quantum al-gorithm which applies the classical convolution method to pattern matching but uses Quantum Fourier Transform for computation of the Discrete Fourier Transform instead of the classical Fast Fourier Transform. Its complexity is analysed and compared to that of the current classical convolution method.

https://pcj.csp.org.ph/index.php/pcj/issue/view/20/PCJ%20V10%20N1%20pp1-9%202015

[Article Title: Permutation Entropy of Card Shuffling/ Guido David, p. 10-13]

Abstract: The classical viewpoint is that seven shuffles are needed to sufficiently randomize a deck of playing cards. On the other hand, according to information theory, six shuffles are sufficient. The numerical shuffling model used in this paper excluded the identity as a possible shuffles, in contrast with other studies. Using Monte Carlo simulations, permutation entropies were numerically calculated for 2 to 9 riffle shuffles. The results show that in the context of entropy, six shuffles are sufficient for randomizing a deck of 52 cards, and five shuffles are acceptable for casual play.

https://pcj.csp.org.ph/index.php/pcj/issue/view/20/PCJ%20V10%20N1%20pp10-13%202015

[Article Title: Notes on Language Relations among Transition P Systems/ Richelle Ann B. Juayong, Henry N. Adorna,Kelvin C. Bu ̃no, and Francis George C. Cabarle, p. 14-21]

Abstract: We explore language relations of specific Transition P (TP) systems without membrane dissolution. The main models we investigate are TP systems having the following characteristic: for every cooperative rule that needs a multiset u, each object a (also called a trigger) in the multiset u can also evolve through a non-cooperative rule defined in the same region. We call such models as TP systems having in-dependent triggers only (or TP-ind systems). A TP system having only non-cooperative rules is a special case of a TP-ind system. In the case of TP-ind system, triggers are said to be independent since every rule trigger can also evolve in-dependently. Otherwise, a (cooperative) rule trigger is said to be dependent. In this paper, we look at characteristics of some TP systems ⇧ with dependent triggers (or TP-dep systems) wherein the language of ⇧ can also be generated by a TP-ind system⇧0.

https://pcj.csp.org.ph/index.php/pcj/issue/view/20/PCJ%20V10%20N1%20pp14-21%202015

[Article Title: Synchronization of ad hoc Clock Networks/ Jaderick P. Pabico, p. 22-32]

Abstract :We introduce a graph-theoretic approach to synchronizing clocks in an adhoc network of N time pieces. Clocks naturally drift away from being synchronized because of many physical factors. The manual way of clock synchronization suffers from an inherrent propagation of the so called “clock drift” due to “word-of-mouth effect.” The current standard way of automated clock synchronization is either via radio band transmission of the global clock or via the software-based Network Time Protocol (NTP). Synchronization via radio band transmission suffers from the wave transmission delay, while the client-server-based NTP does not scale to increased number of clients as well as to unforeseen server overload conditions (e.g., flash crowd and time-of-day effects). Further, the trivial running time of NTP for synchronizing an N-node network, where each node is a clock and the NTP server follows a single-port communication model, is O(N). We introduce in this paper aO (logN) time for synchronizing the clocks in exchange for an increase of O(N) in space complexity, though through creative “tweaking,” we later reduced the space requirement toO(1). Our graph-theoretic protocol assumes that the network is KN, while the subset of clocks are in an embedded circulant graph Cqn<N with q jumps and clock information is communicated through circular shifts within the Cqn<N. All N nodes communicate via a single-port duplex channel model. Theoretically, this synchronization protocol allows for N (log N)−1−1 more synchronizations than the client-server-based one. Empirically through statistically replicated multi-agent-based micro simulation runs, our protocol allows at most 80% of the clocks synchronized compared to the current protocol which only allows up to 30% after some steady-state time.

https://pcj.csp.org.ph/index.php/pcj/issue/view/20/PCJ%20V10%20N1%20pp22-32%202015