Abstract: The invention is directed to apparatus, methods, systems and computer programs which permit a simplification or reduction of the description of a complex digital circuit. This is accomplished by using a completely new system of propositional logic (13B), representing the logic of a logical circuit to be designed as points and vectors in a vector space, simplifying the logic so represented to a simpler form using vector transformations, and designing the circuit using the simpler form. The invention is also directed to apparatus, methods, systems and devices which will implement the vector logic system in optical forms, including free-space optical methods, flat-optical methods, colorimetric methods, and methods using a polarization-based AND-gate.

Abstract: Very complex (multilevel) logical expressions are represented in a vector format. The logic is simplified by identifying opposing couples (a literal and its negation) and replacing symmetrical logic expressions attached to the opposing couples with a single version. Significant simplification of the logic can thus be achieved that is suitable for applications in CAD/CAM and in design and manufacture of integrated circuits. The simplification results in increased reliability, lower cost and faster circuits. Techniques for simplifying circuits with multiple outputs are also described.

Abstract: Very complex (multilevel) logical expressions are represented in a vector format. The logic is simplified by identifying opposing couples (a literal and its negation) and replacing symmetrical logic expressions attached to the opposing couples with a single version. Significant simplification of the logic can thus be achieved that is suitable for applications in CAD/CAM and in design and manufacture of integrated circuits. The simplification results in increased reliability, lower cost and faster circuits.

Abstract: Very complex (multilevel) logical expressions are represented in a vector format. The logic is simplified by identifying opposing couples (a literal and its negation) and replacing symmetrical logic expressions attached to the opposing couples with a single version. Significant simplification of the logic can thus be achieved that is suitable for applications in CAD/CAM and in design and manufacture of integrated circuits. The simplification results in increased reliability, lower cost and faster circuits. Techniques for simplifying circuits with multiple outputs are also described.

Abstract: An optical element for producing an optical NOR gate uses a pair of spatial light modulators or phase shifters and one or more beam splitters to produce outputs representing respectively an XOR function of two control inputs and a COIN function of the two control inputs. The XOR output and the COIN output are combined with a phase shifted version of the source of light used to generate the XOR and COIN outputs to produce both an optical output representing a logical NOR function of the two control inputs. The same circuitry also produces an optical output representing a logical AND function of the two control inputs. The techniques disclosed permit a complete system of optical logic to be produced that can be used to produce an optical processor. The optical logic can advantageously be used in information processing and in communications.

Abstract: Very complex (multilevel) logical expressions are represented in a vector format. The logic is simplified by identifying opposing couples (a literal and its negation) and replacing symmetrical logic expressions attached to the opposing couples with a single version. Significant simplification of the logic can thus be achieved that is suitable for applications in CAD/CAM and in design and manufacture of integrated circuits. The simplification results in increased reliability, lower cost and faster circuits.

Abstract: The invention is directed to apparatus, methods, systems and computer programs which permit a simplification or reduction of the description of a complex digital circuit. This is accomplished by using a completely new system of propositional logic (13B), representing the logic of a logical circuit to be designed as points and vectors in a vector space, simplifying the logic so represented to a simpler form using vector transformations, and designing the circuit using the simpler form. The invention is also directed to apparatus, methods, systems and devices which will implement the vector logic system in optical forms, including free-space optical methods, flat-optical methods, colorimetric methods, and methods using a polarization-based AND-gate.