Takako Soma

Classification of Ternary Logic Functions by Self-Dual Equivalence Classes

Self-dual equivalence class of ternary logic functions is investigated using ternary parametron logic. Based on multiplex or (MUX) realization of a function, a self-dual function is constructed by introducing Gotos self-dualizing variable which feeds constant values to MUX circuit. Self-dual operation is an operation to transform from one function to another among functions realized by different values of self-dualizing variable. It is defined as a combination of permutation group on values and positions of variables and that on values of function. It can be formulated as an exponentiation group by these groups and the equivalence class count is obtained from the cycle index of these groups.

A Multilevel Algorithm for Spectral Partitioning with Extended Eigen-Models

Parallel solution of irregular problems require solving the graph partitioning problem. The extended eigenproblem appears as the solution of some relaxed formulations of the graph partitioning problem. In this paper, a new subspace algorithm for the solving the extended eigenproblem is presented. The structure of this subspace method allows the incorporation of multigrid preconditioners. We numerically compare our new algorithm with a previous algorithm based on Lanczos iteration and show that our subspace algorithm performs better.

Using contour diagrams and JIVE to illustrate object-oriented semantics in the Java programming language

Organick, Forsythe, and Plummer extensively used contour diagrams to illustrate the semantics of procedural and functional programming languages. However, many of the benefits of contour diagrams can still be utilized in explaining the semantics of object-oriented languages and is evident in the software JIVE created by Gestwicki and Jayaraman. This paper illustrates the use of both contour diagrams and JIVE to help students understand passing objects via parameters, returning objects from methods, comparing objects, and using inheritance in the Java programming language. The results from a small informal survey are included. This paper is useful to those teaching Java in a first-year computer science sequence.

Ternary multiway switch and its implementation by neuron-like element

Ternary multiway switch by logic element utilizing third subharmonic oscillation (phasor based ternary logic) can be regarded as a complex-valued neural network. After showing various functions multiway switches can perform, including Fourier transform, by extending the original functionality as a memory address selector, its implementation by neuron-like element is considered as a model of natural neural networks by complex-valued artificial neural networks, and a search for pulse coded phasor signal in the real world is proposed.

A Subspace Semidefinite Programming for Spectral Graph Partitioning

A semidefinite program (SDP) is an optimization problem over n × n symmetric matrices where a linear function of the entries is to be minimized subject to linear equality constraints, and the condition that the unknown matrix is positive semidefinite. Standard techniques for solving SDPs require O(n3) operations per iteration. We introduce subspace algorithms that greatly reduce the cost os solving large-scale SDPs. We apply these algorithms to SDP approximations of graph partitioning problems. We numerically compare our new algorithm with a standard semidefinite programming algorithm and show that our subspace algorithm performs better.

Queues Using Arrays

Unlike stacks where items can only be pushed or popped from the top, a queue has two access points and can only have items added at the rear called enqueue or removed from the front called dequeue. A queue is known as a first-in, first-out or FIFO data structure and is implemented using arrays. A queue is used to simulate a simple scheduler in an operating system in the complete program.

Lists Using Arrays

Unlike stacks that have one access point at the top where an item can be pushed or popped and queues which can only have items enqueued at the rear or dequeued from the front, a list can have items inserted or deleted from the front, rear, or anywhere in between. In this chapter arrays are used to implement ordered lists. The insert and delete methods in addition to the search method are discussed. In the complete program recursion is used to print strings stored in the list.

Stacks and Queues Using References

This chapter revisits stack and queues. Instead of using arrays as done in Chaps. 2 and 3, it uses references to implement the structures which illustrates the ideas of data and procedural abstraction. The chapter also reinforces the ideas presented in Chaps. 5 and 6. The complete program uses a graphical user interface to implement an undo button using a stack.

Lists Using Objects and References

The creation of lists using references and objects is introduced in this chapter. First references and simple objects are reviewed followed by the creation of a node class. Then a simple linked list is created which is then output both iteratively in the test program and recursively in the complete program.

Stacks Using Arrays

Stacks, whose property is known as last-in, first-out or LIFO, is introduced and implemented using arrays. Some of the common operations for stacks such adding and removing an item, push and pop, are discussed. Using stacks, elements in the list can easily be reversed and strings can be checked for a palindrome. Further, prefix and postfix expressions are discussed where postfix expressions can be evaluated using stacks.