This paper proposes 0-1-A-Ā LUT, a new programmable logic using atom switches, and a delay-optimal mapping algorithm for it. Atom switch is a non-volatile memory device of very small geometry which is fabricated between metal layers of a VLSI, and it can be used as a switch device of very small on-resistance and parasitic capacitance. While considerable area reduction of Look Up Tables (LUTs) used in conventional Field Programmable Gate Arrays (FPGAs) has been achieved by simply replacing each SRAM element with a memory element using a pair of atom switches, our 0-1-A-Ā LUT achieves further area and delay reduction. Unlike the conventional atom-switch-based LUT in which all k input signals are fed to a MUX, one of input signals is fed to the switch array, resulting area reduction due to the reduced number of inputs of the MUX from 2k to 2k-1, as well as delay reduction due to reduced fanout load of the input buffers. Since the fanout of this input buffers depends on the mapped logic function, this paper also proposes technology mapping algorithms to select logic function of fewer number of fanouts of input buffers to achieve further delay reduction. From our experiments, the circuit delay using our k-LUT is 0.94% smaller in the best case compared with using the conventional atom-switch-based k-LUT.

Most modern field programmable gate arrays (FPGAs) use a lookup table (LUT) as their basic logic cell. LUT resource requirements increase as O(2k) with an increasing number of inputs, k, so LUTs with more than six inputs negatively affect the overall FPGA performance. To address this problem, we propose a scalable logic module (SLM), which is a logic cell with less configuration memory, by using partial functions of the Shannon expansion for logics that appear frequently. In addition, we develop a technology mapping tool for SLM. The key feature of our tool is to combine a function decomposition process with traditional cut-based mapping. Experimental results show that an SLM-based FPGA with our mapping method uses much fewer configuration memory bits and has a smaller area than conventional LUT-based FPGAs.

This paper describes two speed-up techniques for Boolean matching of LUT-based circuits. One is one-hot encoding technique for variables representing input assignments. Though it requires more variables than existing binary encoding technique, almost all added clauses using one-hot encoding are binary clauses, which are suitable for efficient Boolean constraint propagation. The other is CEGAR (counter example guided abstraction refinement) technique which reduces the CPU time significantly. With both techniques, we can solve Boolean matching problem with 9 input function in 20 milliseconds on average, which is faster than the existing algorithms more than one order of magnitude.

In general-synchronous framework, in which the clock is distributed periodically to each register but not necessarily simultaneously, circuit performance is expected to be improved compared to complete-synchronous framework, in which the clock is distributed periodically and simultaneously to each register. To improve the circuit performance more, logic synthesis for general-synchronous framework is required. In this paper, under the assumption that any clock schedule is realized by an ideal clock distribution circuit, when two or more cell libraries are available, a technology mapping method which assigns a cell to each gate in the given logic circuit by using integer linear programming is proposed. In experiments, we show the effectiveness of the proposed technology mapping method.

Recent technology mappers for LUT based FPGAs employ cut enumeration. Although many cuts are often needed to find a good network, enumerating all the cuts with large size consumes a lot of run-time. Existing algorithms employ the bottom-up merging which calculates Cartesian products of the fanins' cuts for each node. The number of cuts is much smaller than the size of the Cartesian products in most cases. Thus, the existing algorithms are inefficient. Furthermore, the number of cuts exponentially increases with the size of cuts, that makes the run-time much longer. Several algorithms to enumerate not all the cuts but partial cuts have been presented, but they tend to disturb the quality of networks. This paper presents two algorithms to enumerate cuts; an exhaustive enumeration and a partial enumeration. Both of them are efficient because they do not employ the bottom-up merging. The partial enumeration reduces the number of enumerated cuts with a guarantee that a depth-minimum network can be constructed. The experimental results show that the exhaustive enumeration runs about 5 and 13 times faster than the existing bottom-up algorithm for K=8, 9 respectively, while keeping the same results. On the other hand, the partial enumeration runs about 9 and 29 times faster than the existing algorithm for K = 8, 9, respectively. The average area of networks derived by the sets of cuts enumerated by the partial enumeration is only 4% larger than that derived with using all the cuts, and the depth is the same.

The character projection (CP) lithography is utilized for maskless lithography and is a potential for the future photomask fabrication. The drawback of the CP lithography is its low throughput and leads to a price rise of IC devices. This paper discusses a technology mapping technique for enhancing the throughput of the CP lithography. The number of electron beam (EB) shots to project an entire chip directly determines the fabrication time for the chip as well as the throughput of CP equipment. Our technology mapping technique maps EB shot count-effective cells to a circuit in order to increase the throughput of CP equipment. Our technique treats the number of EB shots as an objective to minimize. Comparing with a conventional technology mapping, our technology mapping technique has achieved 26.6% reduction of the number of EB shots for the front-end-of-the-line (FEOL) process without any performance degradation of ICs. Moreover, our technology mapping technique has achieved a 54.6% less number of EB shots under no performance constraints. It is easy for both IC designers and equipment developers to adopt our technique because our technique is a software approach with no additional modification on CP equipment.

This paper presents an efficient technique for solving a Boolean matching problem in cell-library binding, where the number of cells in the library is large. As a basis of the Boolean matching, we use the notion NP-representative (NPR): two functions have the same NPR if one can be obtained from the other by a permutation and/or complementation(s) of the variables. By using a table look-up and a tree-based breadth-first search strategy, our method quickly computes the NPR for a given function. Boolean matching of the given function against the whole library is determined by checking the presence of its NPR in a hash table, which stores NPRs for all the library functions and their complements. The effectiveness of our method is demonstrated through experimental results, which show that it is more than two orders of magnitude faster than the Hinsberger-Kolla's algorithm.

Checking the equivalence of two Boolean functions under permutation of the variables is an important problem in the synthesis of multiplexer-based field-programmable gate arrays (FPGAs), and the problem is known as Boolean matching. This paper presents an efficient breadth-first search technique for computing a canonical form--namely P-representative--of Boolean functions under permutation of the variables. Two functions match if they have the same P-representative. On an ordinary workstation, on the average, the method requires several microseconds to check the Boolean matching of functions with up to eight variables against a library with tens of thousands of cells.

We propose a timing driven gate duplication algorithm for the technology independent phase. Our algorithm is a generalization of the gate duplication strategy suggested in [3]. Our technique gets a more global view by duplicating multiple gates at a time. We compare the minimum circuit delay obtained by SIS with the delay obtained by using our gate duplication. Results show that up to 11% improvement in delay can be obtained. Our algorithm does not have an adverse effect on the overall synthesis time, indicating that gate duplication is an efficient strategy for timing optimization.

This paper presents a CAD technology mapping algorithm for LUT-based FPGAs. Since interconnections in an FPGA must be accomplished with limited routing resources, routability is the most important objective in a technology mapping algorithm. To optimize routability, the goal of the algorithm is the production of a design with a minimum interconnection. The Min-cut algorithm is first used to partition a graph representing a Boolean network into clusters so that the total number of interconnections between clusters is minimum. To decrease further the number of interconnections needed, clusters are then merged into larger clusters by a pairing technique. This algorithm has been tested on the MCNC benchmark circuits. Compared with other LUT-based FPGA mapping algorithms, the algorithm produces better routability characteristics.

Recently, Plastic Cell Architecture (PCA) has been proposed as a hard-wired general-purpose autonomously reconfigurable processor. PCA consists of two layers, the plastic part on which sequential logic circuits are implemented, and the built-in part which induces the plastic part to dynamically reconfigure the circuits and transports messages among the circuits. The plastic part consists of an array of LUT-based reconfigurable logic primitives, each of which is connected only to adjacent ones. Combining logic and layout synthesis, we propose a new array-based algorithm to map logic functions into the PCA plastic part. This algorithm produces a folded array of sum-of-multi-input-complex-terms, especially for the PCA plastic part.

A delay-optimal technology mapping algorithm is developed on a general model of FPGA with hard-wired non-homogeneous logic block architectures which is composed of different sizes of look-up tables (LUTs) hard-wired together. This architecture has the advantages of short delay of hard-wired connections and area-efficiency of non-homogeneous structure. The Xilinx XC4000 is one commercial example, where two 4-LUTs are hard-wired to one 3-LUT. In this paper, we present a two-dimensional labeling approach and a level-2 node cut algorithm to handle the hard-wired feature. The experimental results show that our algorithm generates favorable results for Xilinx XC4000 CLBs. Over a set of MCNC benchmarks, our algorithm produces results with 17% fewer CLB depth than that of FlowMap in similar CPU time on average, and with 4% fewer CLB depth than that of PDDMAP on average while PDDMAP needs 15 times more CPU time.

This paper proposes a fast depth-constrained technology mapping algorithm for logic-blocks composed of tree-structured lookup tables. First, we propose a technology mapping algorithm which minimizes the number of logic-blocks if an input Boolean network is a tree. Second, we propose a technology mapping algorithm which minimizes logic depth for any input Boolean network. Finally, we combine those two technology mapping algorithms and propose an algorithm which realizes technology mapping whose depth is bounded by a given upper bound dc. Experimental results demonstrate the effectiveness and efficiency of the proposed algorithm.

The packing problem is to pack given items into given containers as efficiently as possible under various constraints. It is fundamental and significant with variations and applications. The Set-Bin-Packing (SBP) is a class of packing problems: Pack given items into as few bins which have the same capacity where every item is a set and a bin can contain items as long as the number of distinct elements in the union of the items equals to or less than the capacity. One of applications is in FPGA technology mapping, which is our initial motivation. In this paper, the computational complexity of SBP is studied with respect to three parameters α, γ, and δ which are the capacity, the upper bound of the number of elements in an item, and the upper bound of the number of items having an element, respectively. In contrast that the well known Integer-Bin-Packing (IBP) is NP-hard but is proved that even a simplest heuristics First-Fit-Decreasing (FFD) outputs exact solutions as long as α 6, our result reveals that SBP remains NP-hard for a small values of these parameters. The results are summarized on a 3D map of computational complexities with respect to these three parameters.

This paper proposes "path mapping," a method of delay estimation for technology independent combinational circuits. Path mapping provides fast and accurate delay estimation using common ideas with the tree covering based technology mapping. First, path mapping does technology mapping for all paths in the circuit with minimum mapped delay. Then, it finds the largest mapped delay among all the paths in the circuit, and answers it as an estimated circuit delay. Experimental results show path mapping estimates more accurate circuit delay than unit delay, and runs much faster than the technology mapping.

We present here the Controlling Value Boolean Matching based on fault analysis. The problem is to match a Boolean function with don't cares on library cells under arbitrary input permutations and/or input-output phase assignments. Most of the library cells can be represented by tree structure circuits. The approach presented here is suitable for these structures and computes the Boolean matching better than the structural matching used in SIS. It can handle library cells with a general topology and reconvergent paths. The benchmark test shows that the Controlling Value Boolean Matching can be as facter as the structural matching used in SIS.

This paper presents an FPGA architecture for high-speed systems, such as next-generation B-ISDN telecommunications systems. Such a system requires an LSI in which an over-10K-gate circuit can be implemented and that has a clock cycle rate of 80MHz. So far, the FPGA architecture has only been discussed in terms of its circuit structure. In contrast we consider the circuit structure of the FPGA along with the performance of its dedicated CAD system. We evaluate several FPGA logic-element structures with a technology mapping method. From these experiments, a multiplexor-based logic-element is found to be suitable for implementing such a high-speed circuit using the BDD-based technology mapping method. In addition, we examine how to best utilize the characteristics of the selected logic-cell structure in designing the wiring structure. It is found that the multiplexor-based cell can be connected efficiently in a clustered wiring structure.

The FPGA logic synthesis consists of logic minimization step and technology mapping step. These two steps are usually performed separately to reduce the complexity of the problem. Conventional logic minimization methods try to minimize the number of literals of a given Boolean network, while FPGA technology mapping techniques attempt to minimize the number of basic blocks. However, minimizing the number of literals, which is target architecture-independent feature, does not always lead to minimization of basic block count, which is a FPGA architecture specific feature. Therefore, most of the existing technology mapping systems take into account reorganization of its input circuits to get better mapping results. Such a loosely coupled logic synthesis paradigm may cause difficulties in finding the optimal solution. In this paper, we propose a new logic synthesis approach where logic minimization and technology mapping steps are performed tightly coupled. Our system takes into account FPGA specific features in logic minimization step and thus our technology mapping step does not need to resynthesize the Boolean network. We formulate the technology mapping problem as a graph covering problem. Such formulation provides more global view to optimality and supports versatile cost functions. in addition, a fast and exact library management technique is devised for efficient FPGA cell matching which is one of the most frequently used operations in the FPGA logic synthesis.

Petrify is a tool for (1) manipulating concurrent specifications and (2) synthesis and optimization of asynchronous control circuits. Given a Petri Net (PN), a Signal Transition Graph (STG), or a Transition System (TS) it (1) generates another PN or STG which is simpler than the original description and (2) produces an optimized net-list of an asynchronous controller in the target gate library while preserving the specified input-output behavior. An ability of back-annotating to the specification level helps the designer to control the design process. For transforming a specification petrify performs a token flow analysis of the initial PN and produces a transition system (TS). In the initial TS, all transitions with the same label are considered as one event. The TS is then transformed and transitions relabeled to fulfill the conditions required to obtain a safe irredundant PN. For synthesis of an asynchronous circuit petrify performs state assignment by solving the Complete State Coding problem. State assignment is coupled with logic minimization and speed-independent technology mapping to a target library. The final net-list is guaranteed to be speed-independent, i.e., hazard-free under any distribution of gate delays and multiple input changes satisfying the initial specification. The tool has been used for synthesis of PNs and PNs composition, synthesis and re-synthesis of asynchronous controllers and can be also applied in areas related with the analysis of concurrent programs. This paper provides an overview of petrify and the theory behind its main functions.

A new technology mapping algorithm is developed on a general model of FPGA with composite logic block architectures, consisting of different sizes of look-up tables (LUTs) and possibly different logic gates. In additions, the logic blocks may have hard-wired connections and limit accessible fanouts. Xilinx XC4000 is one example containing LUTs of different sizes and AT&T ORCA is another example containing both LUTs and logic gates. We use a multiple-fanout pattern graph library to model the composite logic block and a premapping technique to generate the subject graph dynamically. A new matching algorithm and a new covering algorithm are also developed for the subject graph covering. The experimental results show that our algorithm is an effective technology mapper for FPGAs with composite logic block architectures, especially for larger circuits. Over a set of MCNC benchmarks, our algorithm requires on the average 4.25% fewer CLBs than PPR, 6.79% fewer CLBs than TEMPT, and 2,79% fewer CLBs than ASYL when used as the XC4000 mapper. Over a set of larger benchmarks, our algorithm outperforms PPR by 13.70%. Very encouraging results were obtained when our algorithm is used as an ORCA mapper, while there was no prior published results.