International Journal of Computer and Information Technology (ISSN: 2279 – 0764) Volume 02– Issue 05, September 2013 www.ijcit.com 1 Digital Equivalence of Biological Neural AND-gate, OR-gate and MIN-Gate Nicoladie D. Tam Department of Biological Sciences University of North Texas Denton, TX 76203 USA Email: nicoladie.tam {at} unt.edu Abstract— This paper provides the mathematical derivation of the equivalent logic gates for spike code processing in neurons. It derives the computational equivalence between the binary code and spike code to illustrate the correspondence between binary and spike code logic operations theoretically. It identifies the similarities and differences between biological neural processing and binary logic gate processing. Using neural spike code for processing, a neuron can be generalized to process the equivalent of a multi-input OR-gate and a multi-input AND-gate by requiring a minimal number of m input spikes (from a set of all n inputs) before firing an output spike. A MIN m -gate is introduced as the equivalent of the generalized multi-input AND m -gate and multi-input OR m -gate that require a minimum of m inputs to fire an output spike. The MIN m -gate is an equivalent of a statistical voting system that processes input spikes with a threshold of a minimum of m ≥ n/2 input spikes for a majority- rule system. Keywords- massively parallel processing, biological neural processing, digital logic gate operation, asynchronous processing I. INTRODUCTION This paper examines the computational equivalence between biological neural circuitries and digital logic so that the similarities and differences between them can be established. Although the similarities between artificial neural networks and digital logic circuitries have been explored [1-4], this paper focuses on addressing the computational equivalence of biological neurons using pulse-coded signals for processing rather than binary-coded signals. The unique computational characteristics using spike-coded signals (a special class of pulse-coded signals) are addressed in this paper, so that the computational equivalence between neural processing and binary processing can be identified. It will be shown below that if spike codes were used in the logic gates (instead of binary code), there exists an equivalent between a multi-input AND-gate and a multi-input OR-gate that can be replaced by a MIN-gate with a minimum threshold of m active inputs out of all total n inputs. Varying the threshold m will provide a majority-rule voting logic gate by a set of generalized AND-gates or OR-gates without requiring any custom-design complex voting VLSI digital logic circuitry [5- 8]. Spike-coded signals can also be processed asynchronously without relying on any external clock pulse for synchronization. II. BINARY CODE VS. SPIKE CODE ENCODING In order to identify the computational differences between a spike-coded signal and binary signal for the subsequent mathematical derivation of the spike code processing logic, a brief review is provided here. The difference between binary- coded signals and spike-coded signals is that binary codes represent time-independent up/down states, whereas spike codes are time-dependent pulse-coded signals the represents a point process. Pulse code uses both pulse width and pulse height to encode information [9]. That is, the time duration of the pulse does encode information (in addition to encode information by the amplitude of the pulse) [10]. In contrast, the time duration of the binary signals does not encode any additional information, since the binary information is encoded in the 0’s and 1’s only (up/down states without any dependence on how long the binary states last in time). The spike code is a special type of binary-coded pulse code in which it takes on the value of 0’s and 1’s (as amplitude), except that the time duration of 1’s is always fixed (a constant t), whereas the duration of 0’s is a variable t. This time- dependent information encoding will result in producing some major differences between how signals are processed and what computations they can perform. III. CHARACTERISTICS OF SPIKE TRAINS The major difference is that spike code encodes the time occurrence of events (by using 1’s to denote the time of occurrence of an event at time t, and 0’s to denote absence of any event). Thus, spike-coded signal is a special class of pulse-coded signal with these distinct characteristics: (1) The occurrences of an event and nonevent information are encoded by the binary code (fixed amplitude signals of 1’s for encoding occurrence of events, and variable time duration of 0’s for encoding non- occurrence of events, respectively); (2) The timing information of the 1’s (spikes) is encoded as the time of occurrence of an event; (3) The timing information of the 0’s (non-spikes) is encoded as silence (period of non-occurrence of events);