Engineering Commons^™

A Quantum Algorithm For Automata Encoding, Edison Tsai, Marek Perkowski

Electrical and Computer Engineering Faculty Publications and Presentations

Encoding of finite automata or state machines is critical to modern digital logic design methods for sequential circuits. Encoding is the process of assigning to every state, input value, and output value of a state machine a binary string, which is used to represent that state, input value, or output value in digital logic. Usually, one wishes to choose an encoding that, when the state machine is implemented as a digital logic circuit, will optimize some aspect of that circuit. For instance, one might wish to encode in such a way as to minimize power dissipation or silicon area. For …

Shift-Symmetric Configurations In Two-Dimensional Cellular Automata: Irreversibility, Insolvability, And Enumeration, Peter Banda, John S. Caughman Iv, Martin Cenek, Christof Teuscher

Mathematics and Statistics Faculty Publications and Presentations

The search for symmetry as an unusual yet profoundly appealing phenomenon, and the origin of regular, repeating configuration patterns have been for a long time a central focus of complexity science, and physics.

Here, we introduce group-theoretic concepts to identify and enumerate the symmetric inputs, which result in irreversible system behaviors with undesired effects on many computational tasks. The concept of so-called configuration shift-symmetry is applied on two-dimensional cellular automata as an ideal model of computation. The results show the universal insolvability of “non-symmetric” tasks regardless of the transition function. By using a compact enumeration formula and bounding the number …

The Quest For Novel Computational Paradigms And Machines, Christof Teuscher

Electrical and Computer Engineering Faculty Publications and Presentations

The quest for novel and unconventional computing machines is mainly motivated by the man-machine dichotomy and by the belief that meeting tomorrow's complex real world challenges will require new paradigms and new engineering methods to organize, train, and program such machines and to interact with them.

Logic Synthesis For Regular Fabric Realized In Quantum Dot Cellular Automata, Marek Perkowski, Alan Mishchenko

Electrical and Computer Engineering Faculty Publications and Presentations

Quantum Dot Cellular Automata are one of the most prospective nano-technologies to build digital circuits. Because of the requirements of only 2 layer wiring and noise avoidance, realizing the circuit in a regular fabrics is even more important for this technology than for classical technologies. In this paper, we propose a regular layout geometry called 3x3 lattice. The main difference of this geometry compared to the known 2x2 lattices is that it allows the cofactors on a level to propagate to three rather than two nodes on the lower level. This gives additional freedom to synthesize compact functional representations. We …

Evolved Reversible Cascades Realized On The Cam-Brain Machine (Cbm), Andrzej Buller, Marek Perkowski

Electrical and Computer Engineering Faculty Publications and Presentations

This paper presents a new approach to reversible cascade evolution based on a 3D cellular automaton. As a research platform we used the ATR's CAMBrain Machine (CBM). Reversible circuits are investigated because they are expected to dissipate much less energy than their irreversible counterparts. One day they will be implemented as nano-scale 3-dimensional chips. A circuit is reversible if the number of its inputs equals the number of its outputs and there is a one-to-one mapping between spaces of input vectors and output vectors. This paper provides: (1) a brief introduction to reversible logic concentrating on definitions and properties of …

Cellular Automata Realization Of Regular Logic, Andrzej Buller, Marek Perkowski

Electrical and Computer Engineering Faculty Publications and Presentations

This paper presents a cellular-automatic model of a reversible regular structure called Davio lattice. Regular circuits are investigated because of the requirement of future (nano-) technologies where long wires should be avoided. Reversibility is a valuable feature because it means much lower energy dissipation. A circuit is reversible if the number of its inputs equals the number of its outputs and there is a one-to-one mapping between spaces of input vectors and output vectors. It is believed that one day regular reversible structures will be implemented as nanoscale 3-dimensional chips. This paper introduces the notion of the Toffoli gate and …

Evolution Of Emergent Computation, James P. Crutchfield, Melanie Mitchell

Computer Science Faculty Publications and Presentations

A simple evolutionary process can discover sophisticated methods for emergent information processing in decentralized spatially-extended systems. The mechanisms underlying the resulting emergent computation are explicated by a novel technique for analyzing particle-based logic embedded in pattern-forming systems. Understanding how globally-coordinated computation can emerge in evolution is relevant both for the scientific understanding of natural information processing and for engineering new forms of parallel computing systems.