It is shown that the time complexity of breaking Data Encryption Standard is O(56) Hadamard gates, O(262272) NOT gates, O(10482) CNOT gates, O(458880) CCNOT gates, O(1) Shor's quantum order-finding algorithm, and O(1) measurement, and the space complexity of breaking Data Encryption Standard is O(3367) quantum bits.

We demonstrate that the logic computation performed by the DNA-based algorithm for solving general cases of the satisfiability problem can be implemented by our proposed quantum algorithm on the quantum machine proposed by Deutsch. Moreover, we also prove that the logic computation by the bio-molecular operations proposed by Adleman can be implemented by quantum gates (for example, the Hadamard gate, NOT, CNOT, and CCNOT) on the quantum machine. Furthermore, those NP-complete problems solved on a bio-molecular computer are also solvable on a quantum computer. To test our theory, we carry out a three-qubit NMR experiment for solving the simplest satisfiability problem.

We propose three DNA-based algorithms - parallel subtractor, parallel comparator and parallel modular arithmetic - that formally verify our designed molecular solutions for factoring the product of two large prime numbers.

Data alignment that facilitates data locality so that the data access communication costs can be minimized, helps distributed memory parallel machines improve their throughput. Most data alignment methods are devised mainly to align the arrays referenced using linear subscripts or quadratic subscripts with few (one or two) loop index variables. We propose two communication-free alignment techniques to align the arrays referenced using linear subscripts or quadratic subscripts with multiple loop index variables. The experimental results from our techniques on vector loop and TRFD of the perfect benchmarks reveal that our techniques can improve the execution times of the subroutines in these benchmarks.

In this paper, WC proposed the infinity Lambda test.The infinity Lambda test can be applied IO deal with data dependence of coupled arrays with symbolic (urrknowr, at compile time) bounds.Experimental data reflecting the effect of the infinity Lambda test are also presented.