Discrete functions are now commonly represented by binary (BDD) and multiple-valued (MDD) decision diagrams. Sifting is an effective heuristic technique which applies adjacent variable interchanges to find a good variable ordering to reduce the size of a BDD or MDD. Linear sifting is an extension of BDD sifting where XOR operations involving adjacent variable pairs augment adjacent variable int...

In this paper a gate-level evolvable hardware technique for designing multiple-valued (MV) combinational circuits is proposed for the first time. In comparison with the decomposition techniques used for synthesis of combinational circuits previously employed, this new approach is easily adapted for the different types of MV gates associated with operations corresponding to different algebra typ...

Development of large computerized systems requires both combinational and sequential circuits. Registers and counters are two important examples of sequential circuits, which are widely used in practical applications like CPUs. The basic element of sequential logic is Flip-Flop, which stores an input value and returns two outputs (Q and Q ). This paper presents an innovative ternary D Flip-Flap...

We analyze the computational complexity of the cost-table approach to designing multiple-valued logic circuits that is applicable to IL, CCDs, current-mode CMOS, and RTDs. We show that this approach is NP-complete. An efficient algorithm is shown for finding the exact minimal realization of a given function by a given cost-table.

We propose the use of universal literals as a means of reducing the cost of multiple-valued circuits. A universal literal is any function on one variable. The target architecture is a sum-of-products structure, where sum is the truncated sum and product terms consist of the minimum of universal literals. A significant cost reduction is demonstrated over the conventional window literal. The prop...

A novel architecture f o r a Multiple-Valued Ferroelectric Content-Addressable Memory (FCAM) is proposed. An FCAM employs ferroelectric capacitors as storage elements to provide a nonvolatile content-addressable memory. A 2-bit search operation is performed by a simultaneous access to a 4-level polarization, hence reducing the total number of search operations to h a y Four FCAM structures are ...

Decision diagrams are the state-of-the-art representation for logic functions, both binary and multiple-valued. Here we consider issues regarding the efficient implementation of a package for the creation and manipulation of multiple-valued decision diagrams (MDDs). In particular, we identify issues that differ from binary decision diagram packages. We describe a matrix method for level interch...

Signed clausal forms offer a suitable logical framework for automated reasoning in multiple-valued logics. It turns out that the satisfiability problem of any finitely-valued propositional logic, as well as of certain infinitely-valued logics, can be easily reduced, in polynomial time, to the satisfiability problem of signed clausal forms. On the other hand, signed clausal forms are a powerful ...

We consider functions of the form f : are only partially speciied. In general, f assigns to any output y i a nonempty set d 2 D of elements of E. If d = feg for some e 2 E, then y i has the value e. If d = E, then y i is a \complete don't care", i.e., is allowed to take on any value in E. In other cases, y i is a \limited don't care", allowed to take on any value in d. Moreover, the functions a...

The Archimedean property is one of the most beautiful axioms of the classical arithmetic and some of the methods of constructing the field of real numbers are based on this property. It is well-known that every Archimedean `-group is abelian and every pseudo-MV algebra is commutative. The aim of this paper is to introduce the Archimedean property for pseudo-MTL algebras and FLw-algebras. The ma...