We show that, over Q, if an n-variate polynomial of degree d = nO(1) is computable by an arithmetic circuit of size s (respectively by an algebraic branching program of size s) then it can also be computed by a depth three circuit (i.e. a ΣΠΣ-circuit) of size exp(O( √ d log d log n log s)) (respectively of size exp(O( √ d log n log s))). In particular this yields a ΣΠΣ circuit of size exp(O( √ ...

The use of Cloud Computing has increasedrapidly in many organization .Cloud Computing provides many benefits in terms of low cost and accessibility of data. In addition Cloud Computing was predicted to transform the computing world from using local applications and storage into centralized services provided by organization.[10] Ensuring the security of Cloud Computing is major factor in the Clo...

The use of Cloud Computing has increasedrapidly in many organization .Cloud Computing provides many benefits in terms of low cost and accessibility of data. In addition Cloud Computing was predicted to transform the computing world from using local applications and storage into centralized services provided by organization.[10] Ensuring the security of Cloud Computing is major factor in the Clo...

The advantages of quantum computing as compared to classical computing are currently being researched; therefore, the ability to correctly simulate quantum circuits is becoming increasingly more important. A Quantum Multiple-valued Decision Diagram, or QMDD, is a structure which allows for an efficient implementation of a quantum circuit simulator. This structure can be used to create a quantum...

Quantum computing is gaining serious momentum in these days. With increasing capabilities of corresponding devices also comes the need for efficient and automated tools to design them. Verification, i.e., ensuring that originally intended functionality a quantum algorithm/circuit preserved throughout all layers abstraction during process, vital part software stack. In this work, we present QCEC...

We investigate computing models that are presented as families of finite computing devices with a uniformity condition on the entire family. Examples of such models include Boolean circuits, membrane systems, DNA computers, chemical reaction networks and tile assembly systems, and there are many others. However, in such models there are actually two distinct kinds of uniformity condition. The f...

The development of conventional computing technologies faces many challenges for the last couple of decades. Power dissipation in today's computer chips becomes dominant. Reversible computing is a promising alternative to these technologies, with applications in ultra-low power, nano computing, quantum computing, low power CMOS design, optical information processing, bioinformatics etc. In...

DNA computing has recently gained intensive attention as an emerging field bridging the gap between computer science and biomolecular science. DNA based computing can be competitively used to simulate various computing models including Boolean circuits because of its potential to offer massive parallelism. In this paper we present a new DNA-based evaluation algorithm for a bounded fan-in circui...

Functional decomposition aims at finding efficient representations for Boolean functions. It is used in many applications, including multi-level logic synthesis, formal verification, and testing. This dissertation presents novel heuristic algorithms for functional decomposition. These algorithms take advantage of suitable representations of the Boolean functions in order to be efficient. The fi...