Boolean domain

Abstract: UNLABELLED A theory is presented that attempts to answer two questions. What visual contents can an observer consciously access at one moment? ANSWER only one feature value (e.g., green) per dimension, but those feature values can be associated (as a group) with multiple spatially precise locations (comprising a single labeled Boolean map). How can an observer voluntarily select what to access? ANSWER in one of two ways: (a) by selecting one feature value in one dimension (e.g., selecting the color red) or (b) by iteratively combining the output of (a) with a preexisting Boolean map via the Boolean operations of intersection and union. Boolean map theory offers a unified interpretation of a wide variety of visual attention phenomena usually treated in separate literatures. In so doing, it also illuminates the neglected phenomena of attention to structure.

Abstract: The switch-level model represents a digital metal-oxide semiconductor (MOS) circuit as a network of charge storage nodes connected by resistive transistor switches. The functionality of such a network can be expressed as a series of systems of Boolean equations. Solving these equations symbolically yields a set of Boolean formulas that describe the mapping from input and current state to the new network states. This analysis supports the same class of networks as the switch-level simulator MOSSIM II and provides the same functionality, including the handling of bidirectional effects and indeterminate (X) logic values. In the worst case, the analysis of an n-node network can yield a set of formulas containing a total of O(n /sup 3/) operations. However, all but a limited set of dense, pass-transistor networks give formulas with O(n) total operations. The analysis can serve as the basis of efficient programs for a variety of logic design tasks, including logic simulation (on both conventional and special-purpose computers), fault simulation, test generation, and symbolic verification.

Abstract: This paper investigates the structure of Boolean networks via input-state structure. Using the algebraic form proposed by the author, the logic-based input-state dynamics of Boolean networks, called the Boolean control networks, is converted into an algebraic discrete-time dynamic system. Then the structure of cycles of Boolean control systems is obtained as compounded cycles. Using the obtained input-state description, the structure of Boolean networks is investigated, and their attractors are revealed as nested compounded cycles, called rolling gears. This structure explains why small cycles mainly decide the behaviors of cellular networks. Some illustrative examples are presented.

Abstract: In this paper, we present Majority-Inverter Graph (MIG), a novel logic representation structure for efficient optimization of Boolean functions. An MIG is a directed acyclic graph consisting of three-input majority nodes and regular/complemented edges. We show that MIGs include any AND/OR/Inverter Graphs (AOIGs), containing also the well-known AIGs. In order to support the natural manipulation of MIGs, we introduce a new Boolean algebra, based exclusively on majority and inverter operations, with a complete axiomatic system. Theoretical results show that it is possible to explore the entire MIG representation space by using only five primitive transformation rules. Such feature opens up a great opportunity for logic optimization and synthesis. We showcase the MIG potential by proposing a delay-oriented optimization technique. Experimental results over MCNC benchmarks show that MIG optimization reduces the number of logic levels by 18%, on average, with respect to AIG optimization performed by ABC academic tool. Employed in a traditional optimization-mapping circuit synthesis flow, MIG optimization enables an average reduction of {22%, 14%, 11%} in the estimated {delay, area, power} metrics, before physical design, as compared to academic/commercial synthesis flows.