The Architectures of GeneXproTools Learning Algorithms

Built-in Logical Functions

 Below are listed all the 258 built-in logical functions available in GeneXproTools 4.0, starting with their representation in Karva Notation and their logical definition (for more details about their implementations, see the built-in grammars of GeneXproTools): Basic logical functions with 1 and 2 inputs: Not: A' And: A·B Or: A+B Nand: (A·B)' Nor: (A+B)' Xor: A^B Nxor: (A^B)' Basic logical functions with 3 inputs: And3: A·B·C Or3: A+B+C Nand3: (A·B·C)' Nor3: (A+B+C)' Odd3: Odd-3-parity Even3: Even-3-parity Basic logical functions with 4 inputs: And4: A·B·C·D Or4: A+B+C+D Nand4: (A·B·C·D)' Nor4: (A+B+C+D)' Odd4: Odd-4-parity Even4: Even-4-parity Additional logical functions with 1 input: Id: Id(A) = A Zero: 0(A) = 0 One: 1(A) = 1 Additional logical functions with 2 inputs: LT: A < B GT: A > B LOE: A <= B GOE: A >= B NotA: NOT(A,B) = NOT A NotB: NOT(A,B) = NOT B IdA: IdA(A,B) = A IdB: IdB(A,B) = B Zero2: 0(A,B) = 0 One2: 1(A,B) = 1 Derived logical functions with 3 inputs: LT3: A < B < C GT3: A > B > C LOE3: A <= B <= C GOE3: A >= B >= C Common logical functions with 3 inputs: Mux: 3-Multiplexer If: If A = 1, then B, else C Maj: Majority(A,B,C) Min: Minority(A,B,C) 2Off: Exactly two off 2On: Exactly two on Universal logical modules with 3 inputs (series A): LM3A1: AC'+BC LM3A2: AC'+B'C LM3A3: A'C'+BC LM3A4: A'C'+B'C Universal logical modules with 3 inputs (series B): LM3B1: (A+C')·(B+C) LM3B2: (A+C')·(B'+C) LM3B3: (A'+C')·(B+C) LM3B4: (A'+C')·(B'+C) Universal logical modules with 3 inputs (series C): LM3C1: AB'+BC LM3C2: AB'+ BC' LM3C3: A'B'+BC LM3C4: A'B'+ BC' Universal logical modules with 3 inputs (series D): LM3D1: (A+B')·(B+C) LM3D2: (A+B')·(B+C') LM3D3: (A'+B')·(B+C) LM3D4: (A'+B')·(B+C') Universal logical modules with 3 inputs (series E): LM3E1: A'C+ AB' LM3E2: A'C'+AB LM3E3: A'C'+ AB' Universal logical modules with 3 inputs (series F): LM3F1: (A'+C)·(A+B') LM3F2: (A'+C')·(A+B) LM3F3: (A'+C')·(A+B') Universal logical modules with 3 inputs (series G): LM3G1: (A^C')·(B^C) LM3G2: (A^C')·(B'^C) LM3G3: (A'^C')·(B^C) LM3G4: (A'^C')·(B'^C) Universal logical modules with 3 inputs (series H): LM3H1: ((A·B)'· C)' LM3H2: (A·(B·C)')' LM3H3: ((A+B)'+ C)' LM3H4: (A+(B+C)')' Comparison IF THEN ELSE functions with 3 inputs (series A): LT3A: If A < B, then (A·C), else (B·C)' GT3A: If A > B, then (A·C), else (B·C)' LOE3A: If A <= B, then (A·C), else (B·C)' GOE3A: If A >= B, then (A·C), else (B·C)' ET3A: If A = B, then (A·C), else (B·C)' NET3A: If A != B, then (A·C), else (B·C)' Comparison IF THEN ELSE functions with 3 inputs (series B): LT3B: If A < B, then (A·C)', else (A·C) GT3B: If A > B, then (A·C)', else (A·C) LOE3B: If A <= B, then (A·C)', else (A·C) GOE3B: If A >= B, then (A·C)', else (A·C) ET3B: If A = B, then (A·C)', else (A·C) NET3B: If A != B, then (A·C)', else (A·C) Comparison IF THEN ELSE functions with 3 inputs (series C): LT3C: If A < B, then (A+C)', else (B+C) GT3C: If A > B, then (A+C)', else (B+C) LOE3C: If A <= B, then (A+C)', else (B+C) GOE3C: If A >= B, then (A+C)', else (B+C) ET3C: If A = B, then (A+C)', else (B+C) NET3C: If A != B, then (A+C)', else (B+C) Additional universal logical modules with 3 inputs: T004: 00000100 T008: 00001000 T009: 00001001 T032: 00100000 T033: 00100001 T041: 00101001 T055: 00110111 T057: 00111001 T064: 01000000 T065: 01000001 T069: 01000101 T073: 01001001 T081: 01010001 T089: 01011001 T093: 01011101 T096: 01100000 T101: 01100101 T109: 01101101 T111: 01101111 T121: 01111001 T123: 01111011 T125: 01111101 T154: 10011010 T223: 11011111 T239: 11101111 T249: 11111001 T251: 11111011 T253: 11111101 Derived logical functions with 4 inputs: LT4: A < B < C < D GT4: A > B > C > D LOE4: A <= B <= C <= D GOE4: A >= B >= C >= D Common logical functions with 4 inputs: Tie: Tie Ntie: Not tie 3Off: Exactly three off 3On: Exactly three on Universal logical modules with 4 inputs (series A): LM4A1: AD'+BD+CD LM4A2: AD'+B'D+CD LM4A3: AD'+BD+C'D LM4A4: AD'+B'D+C'D LM4A5: A'D'+BD+CD LM4A6: A'D'+B'D+CD LM4A7: A'D'+BD+C'D LM4A8: A'D'+B'D+C'D Universal logical modules with 4 inputs (series B): LM4B1: (A+D')·(B+D)·(C+D) LM4B2: (A+D')·(B'+D)·(C+D) LM4B3: (A+D')·(B+D)·(C'+D) LM4B4: (A+D')·(B'+D)·(C'+D) LM4B5: (A'+D')·(B+D)·(C+D) LM4B6: (A'+D')·(B'+D)·(C+D) LM4B7: (A'+D')·(B+D)·(C'+D) LM4B8: (A'+D')·(B'+D)·(C'+D) Universal logical modules with 4 inputs (series C): LM4C1: AB'+BC+BD LM4C2: AB'+B'C+BD LM4C3: AB'+BC+B'D LM4C4: AB'+B'C+B'D LM4C5: A'B'+BC+BD LM4C6: A'B'+B'C+BD LM4C7: A'B'+BC+B'D LM4C8: A'B'+B'C+B'D Universal logical modules with 4 inputs (series D): LM4D1: (A+B')·(B+C)·(B+D) LM4D2: (A+B')·(B'+C)·(B+D) LM4D3: (A+B')·(B+C)·(B'+D) LM4D4: (A+B')·(B'+C)·(B'+D) LM4D5: (A'+B')·(B+C)·(B+D) LM4D6: (A'+B')·(B'+C)·(B+D) LM4D7: (A'+B')·(B+C)·(B'+D) LM4D8: (A'+B')·(B'+C)·(B'+D) Universal logical modules with 4 inputs (series E): LM4E1: AC'+BC+CD LM4E2: AC'+B'C+CD LM4E3: AC'+BC+C'D LM4E4: AC'+B'C+C'D LM4E5: A'C'+BC+CD LM4E6: A'C'+B'C+CD LM4E7: A'C'+BC+C'D LM4E8: A'C'+B'C+C'D Universal logical modules with 4 inputs (series F): LM4F1: (A+C')·(B+C)·(C+D) LM4F2: (A+C')·(B'+C)·(C+D) LM4F3: (A+C')·(B+C)·(C'+D) LM4F4: (A+C')·(B'+C)·(C'+D) LM4F5: (A'+C')·(B+C)·(C+D) LM4F6: (A'+C')·(B'+C)·(C+D) LM4F7: (A'+C')·(B+C)·(C'+D) LM4F8: (A'+C')·(B'+C)·(C'+D) Universal logical modules with 4 inputs (series G): LM4G1: A'D+AB+AC LM4G2: A'D+AB'+AC LM4G3: A'D+AB+ AC' LM4G4: A'D+AB'+ AC' LM4G5: A'D'+AB+AC LM4G6: A'D'+AB'+AC LM4G7: A'D'+AB+ AC' LM4G8: A'D'+AB'+ AC' Universal logical modules with 4 inputs (series H): LM4H1: (A'+D)·(A+B)·(A+C) LM4H2: (A'+D)·(A+B')·(A+C) LM4H3: (A'+D)·(A+B)·(A+C') LM4H4: (A'+D)·(A+B')·(A+C') LM4H5: (A'+D')·(A+B)·(A+C) LM4H6: (A'+D')·(A+B')·(A+C) LM4H7: (A'+D')·(A+B)·(A+C') LM4H8: (A'+D')·(A+B')·(A+C') Universal logical modules with 4 inputs (series I): LM4I1: (((A·B)'·C)'· D)' LM4I2: (A·(B·(C·D)')')' LM4I3: ((A·(B· C)')'·D)' LM4I4: (A·((B·C)'· D)')' LM4I5: (((A+B)'+C)'+ D)' LM4I6: (A+(B+(C+D)')')' LM4I7: ((A+(B+ C)')'+D)' LM4I8: (A+((B+C)'+ D)')' Comparison IF THEN ELSE functions with 4 inputs (series A): LT4A: If A < B, then C, else D GT4A: If A > B, then C, else D LOE4A: If A <= B, then C, else D GOE4A: If A >= B, then C, else D ET4A: If A = B, then C, else D NET4A: If A != B, then C, else D Comparison IF THEN ELSE functions with 4 inputs (series B): LT4B: If A < B, then (C·D), else D' GT4B: If A > B, then (C·D), else D' LOE4B: If A <= B, then (C·D), else D' GOE4B: If A >= B, then (C·D), else D' ET4B: If A = B, then (C·D), else D' NET4B: If A != B, then (C·D), else D' Comparison IF THEN ELSE functions with 4 inputs (series C): LT4C: If A < B, then (C+D), else D' GT4C: If A > B, then (C+D), else D' LOE4C: If A <= B, then (C+D), else D' GOE4C: If A >= B, then (C+D), else D' ET4C: If A = B, then (C+D), else D' NET4C: If A != B, then (C+D), else D' Comparison IF THEN ELSE functions with 4 inputs (series D): LT4D: If A < B, then (A·D), else (C·D)' GT4D: If A > B, then (A·D), else (C·D)' LOE4D: If A <= B, then (A·D), else (C·D)' GOE4D: If A >= B, then (A·D), else (C·D)' ET4D: If A = B, then (A·D), else (C·D)' NET4D: If A != B, then (A·D), else (C·D)' Comparison IF THEN ELSE functions with 4 inputs (series E): LT4E: If A < B, then (A·D)', else (A·C) GT4E: If A > B, then (A·D)', else (A·C) LOE4E: If A <= B, then (A·D)', else (A·C) GOE4E: If A >= B, then (A·D)', else (A·C) ET4E: If A = B, then (A·D)', else (A·C) NET4E: If A != B, then (A·D)', else (A·C) Additional universal logical modules with 4 inputs: Q0002: 0000000000000010 Q001C: 0000000000011100 Q0048: 0000000001001000 Q0800: 0000100000000000 Q3378: 0011001101111000 Q3475: 0011010001110101 Q3CB0: 0011110010110000 Q3DEF: 0011110111101111 Q3DFF: 0011110111111111 Q4200: 0100001000000000 Q4C11: 0100110000010001 Q5100: 0101000100000000 Q5EEF: 0101111011101111 Q5EFF: 0101111011111111 Q6A6D: 0110101001101101 Q6F75: 0110111101110101 Q74C4: 0111010011000100 Q7DA3: 0111110110100011 Q8304: 1000001100000100 Q8430: 1000010000110000 Q8543: 1000010101000011 Q9D80: 1001110110000000 QA092: 1010000010010010 QB36A: 1011001101101010 QCBCF: 1100101111001111 QEEB1: 1110111010110001 QEFFF: 1110111111111111 QFF7B: 1111111101111011 QFFF6: 1111111111110110 QFFFB: 1111111111111011 Dynamic UDFs are indexed and are represented by: DDF0 DDF1 etc. Static UDFs are also indexed and are represented by: UDF0 UDF1 etc.
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