Lattice Structure of Some Closed Classes for Three-Valued Logic and Its Applications

This paper provides a brief overview of modern applications of nonbinary logic models, where the design of heterogeneous computing systems with small computing units based on three-valued logic produces a mathematically better and more effective solution compared to binary models. For application, it is necessary to implement circuits composed of chipsets, the operation of which is based on three-valued logic. To be able to implement such schemes, a fundamentally important theoretical problem must be solved: the problem of completeness of classes of functions of three-valued logic. From a practical point of view, the completeness of the class of such functions ensures that circuits with the desired operations can be produced from an arbitrary (finite) set of chipsets. In this paper, the closure operator on the set of functions of three-valued logic that strengthens the usual substitution operator is considered. It is shown that it is possible to recover the sublattice of closed classes in the general case of closure of functions with respect to the classical superposition operator. The problem of the lattice of closed classes for the class of functions T2 preserving two is considered. The closure operators R1 for the functions that differ only by dummy variables are considered equivalent. This operator is withiin the scope of interest of this paper. A lattice is constructed for closed subclasses in T2={f|f(2,…,2)=2}, a class of functions preserving two.

MARCO: A High-performance Task M apping a nd R outing Co -optimization Framework for Point-to-Point NoC-based Heterogeneous Computing Systems

Heterogeneous computing systems (HCSs), which consist of various processing elements (PEs) that vary in their processing ability, are usually facilitated by the network-on-chip (NoC) to interconnect its components. The emerging point-to-point NoCs which support single-cycle-multi-hop transmission, reduce or eliminate the latency dependence on distance, addressing the scalability concern raised by high latency for long-distance transmission and enlarging the design space of the routing algorithm to search the non-shortest paths. For such point-to-point NoC-based HCSs, resource management strategies which are managed by compilers, scheduler, or controllers, e.g., mapping and routing, are complicated for the following reasons: (i) Due to the heterogeneity, mapping and routing need to optimize computation and communication concurrently (for homogeneous computing systems, only communication). (ii) Conducting mapping and routing consecutively cannot minimize the schedule length in most cases since the PEs with high processing ability may locate in the crowded area and suffer from high resource contention overhead. (iii) Since changing the mapping selection of one task will reconstruct the whole routing design space, the exploration of mapping and routing design space is challenging. Therefore, in this work, we propose MARCO, the m apping a nd r outing co -optimization framework, to decrease the schedule length of applications on point-to-point NoC-based HCSs. Specifically, we revise the tabu search to explore the design space and evaluate the quality of mapping and routing. The advanced reinforcement learning (RL)algorithm, i.e., advantage actor-critic, is adopted to efficiently compute paths. We perform extensive experiments on various real applications, which demonstrates that the MARCO achieves a remarkable performance improvement in terms of schedule length (+44.94% ∼ +50.18%) when compared with the state-of-the-art mapping and routing co-optimization algorithm for homogeneous computing systems. We also compare MARCO with different combinations of state-of-the-art mapping and routing approaches.