We present a comprehensive and universal quantum computing model based on 2-qubit measurements (TQC), which embeds trivially in a model based on 1-qubit measurements known as the one-way model (1WQC). One inherits through this embedding a calculus whereby each TQC computing pattern can be put in a standard form where entanglement is done first, then measurement, then local corrections.

Many of the popular Merkle-Damg̊ard hash functions have turned out to be not collision-resistant (CR). The problem is that we no longer know if these hash functions are even second-preimage-resistant (SPR) or one-way (OW), without the underlying compression functions being CR. We remedy this situation by introducing the “split padding” into a current Merkle-Damg̊ard hash function H. The patched h...

On every n-long input, every two-way finite automaton (fa) can reverse its input head O(n) times before halting. A fawith few reversals is an automaton where this number is only o(n). For every h, we exhibit a language that can be recognized by an h-state nondeterministic fa with few reversals, but requires Ω(2) states on every deterministic fa with few reversals.

optimization is an important methodology for activities in planning and design. the transportation designers are able to introduce better projects when they can save time and cost of travel for project by optimization methods. most of the optimization problems in engineering are more complicated than they can be solved by custom optimization methods. the most common and available methods are he...