A design system for a special purpose processor executing algorithms described by high level language is discussed. The system can generate an optimized architecture for the processor and also supply a specialized high level language compiler for the processor. A new optimization procedure is introduced to find effective functional blocks that can contribute to the improvement of performance. Functional blocks are found by simulation of the frequently appearing patterns of execution in the algorithm and used to yield a useful combined instruction.

The throughput of a parallel execution of a Digital Signal Processing (DSP) algorithm is limited by the iteration bound, which is the minimum period between the start of consecutive iterations. It is given by T=max (T_i/D_i), where T_i and D_i are the total time of operations and the number of delays in loop i, respectively. A schedule is said rate-optimal if its iteration period is T. The throughput of a DSP algorithm execution can be increased by reducing the T_i's, which can be done by taking as many operations as possible out of loops without changing the semantic of the calculation. This paper presents an optimization technique, called Loop Shrinking, which reduces the iteration bound this way by using commutativity, associativity and distributivity. Also, this paper presents a scheduling method, called Period-Driven Scheduling, which gives rate-optimal schedules more efficiently than existing approaches. An implementation of both is then presented for a system in development by the authors. The system shows reduction in the iteration bound near or equal to careful hand-tunning, and hardware-optimal designs in most of the cases.

In recent VLSI design of digital data paths, significantly more area is occupied by interconnect elements than by functional units and registers. Nevertheless, until recently most work in data path synthesis has been concentrated on trying to reduce the area of functional units and registers, without paying much attention to the interconnect area. Lately, research that addresses reducing the area of interconnection and of functional units and registers is increasing, but in them, most algorithms for assigning interconnect elements are not efficient enough to optimize the interconnect area. In most current research, algorithms for interconnect element assignment are used to calculate the cost functions during the scheduling and/or allocation steps. This makes it impossible to use efficient optimization algorithms that may consume long time. This paper presents some new algorithms used to assign interconnect elements in data paths. The algorithms minimize the number of multiplexer inputs after the scheduling and operator/register allocations have been made. The algorithms have two characteristics. First, we use a branch and bound method for small problems. We confirmed that exact solutions in practical time can be obtained with this method for rather large problems, when the solutions are restricted to a one-level multiplexer model. Second, we use a certain heuristic method for larger problems. The algorithms have been implemented in C on an Apollo Domain Series 10000.

Boolean unification is an algorithm to obtain the general solution of a given Boolean equation. Since a general solution provides a way to represent a complete don't care set, Boolean unification can be a powerful technique when applied to logic synthesis. In this paper we present various applications of Boolean unification to combinational logic synthesis. Three topics of combinational logic synthesis: redesign, multi-level logic minimization and minimization of Boolean relations are discussed. All these problems can be uniformly formalized as Boolean equations. Experimental results are also reported.

Recently, Burch et al. proposed symbolic model checking method to verify sequential machines formally. The method, which is based on logic function manipulation using binary decision diagram, can handle large sequential machines that cannot be handled by the conventional techniques. The expressive power of Computational Tree Logic (CTL), which was used by Burch et al., is not very powerful, for example, CTL cannot describe repetition of events. This papers shows an extension of the symbolic model checking algorithm to Branching time regular temporal logic (BRTL), which has been proposed by the authors as an improvement of CTL in terms of expressive power. The implemented verifier based on the proposed algorithm could verify behaviors of a microprocessor composed of approximately 1,600 gates and 68 flipflops.

The paper proposes a combined delay model to manipulate the variance of the delay time of logic elements and a new timing verification method based on the theory of regular expressions. With the delay time of logic elements such as TTL SN7400, the minimum delay time (d_m), the maximum delay time (d_M), and the typical delay time are specified in the manual, and the delay time of an element is one in the interval between d_m and d_M. Here we assume a discrete time, and we manipulate the variance of the delay time as a set of output strings corresponding to each delay time. We call the model as the combined delay model. Since many output strings are generated with a single input string, the usual timing simulation method cannot be applied. We propose a timing verification method using a behavior extraction method of logic circuits with respect to a time string set: with respect to the specified input set, the method extracts the output string set of each element in the circuit. We devised (1) a mechanism to keep the correspondence between a primary input string and an output string with respect to the primary input string, (2) a mechanism to manipulate the nondeterminism included in the combined delay model, and (3) an event-driven like data compaction method in representing finite automata. We focused on the hazard detection problem and the verification of asynchronous circuits, and show the effectiveness of our method with medium sized circuit with 100 elements or so. The method includes the state explosion, but the data compaction method and the extraction for only the specified input set are useful to control the state explosion.

Behavioral extraction from circuit description is a useful technique for logic design verification. We have proposed a technique of extraction from combinational circuits and developed a prototype system. To use this system practically, it is necessary to deal with sequential circuits. In this paper, we will present a new technique to extract behavioral descriptions from synchronous sequential circuits which include some flip-flops. Flip-flops are classified to two types. The one is a part of control registers. The other is a part of data registers. Behavior of the circuit with control registers is described by the state transition. Behavior of the circuit with data registers is described by the movement of data among registers. There are many circuits, as micro processors, which realize a function after some times of state transitions occurred. In such circuits, it is more important to abstract the function than to extract each state transition. We have progressed our system to extract such behaviors.

In this paper we propose a new timing verification technique named coded time-symbolic simulation, CTSS. Our interest is on simulation of logic circuits consisting of gates whose delay is specified only by its minimum and maximum values. Conventional logic simulation based on min/max delay model leads to over-pessimistic results. In our new method, the cases of possible delay values of each gate are encoded by binary vectors. The circuit behavior for all the possible combinations of the delay values are simulated based on symbolic simulation by assigning Boolean variables to the binary vectors. This simulation technique can deal with logic circuits containing feedback loops as well as combinational circuits. We implemented an efficient simulator by using shared binary decision diagrams (SBDD's) as internal representation of Boolean functions. We also propose novel techniques of analyzing the results of CTSS.

The paper describes a parallel algorithm for the manipulation of binary decision diagrams on a shared memory multi-processor system. Binary decision diagrams are very efficient representations of logic functions, and are widely used in computer aided design of logic circuits. Logic operations on logic functions such as AND and OR are reduced to operations on binary decision diagrams representing these functions. Operations on binary decision diagrams are time-consuming in some cases, and a fast manipulation method is needed. As with the manipulation, we focus on the construction of a binary decision diagram from a logic formula, and devised a parallel algorithm for the construction. In the construction, there are many logic operations to be processed, and some of them can be processed in parallel. At first, we introduce an extraction method and a parallel-execution method for such parallelizable operations. This is the parallel execution method for an operation sequence (or a set of operations). To extract more parallelism, we introduce a dynamic expansion method of a logic operation. The dynamic expansion is a method to obtain sub-operations from a logic operation using the modified Shannon's expansion. These sub-operations are executed in parallel and the results of these sub-operations are merged to obtain the result of the original operation. Our parallel algorithm, which is based on the construction of shared binary decision diagrams with the negative edge and the operation cache, is implemented in C on a shared memory multi-processor system Sequent S-81 (CPU 80386 (16 MHz)28, 86.75MB), and applied to multiplier examples and ISCAS benchmarks. The speed-up ratio becomes 14 for multipliers, and becomes 11 for c1908 in ISCAS benchmarks.

This paper presents the EXM-algorithm, which locates multiple logic design errors in a combinational circuit with multiple output. The error possibility index and the six-valued simulation method have been enhanced to be applied to multiple output circuit. The algorithm locates multiple errors even if they belong to different cone circuits, and processes faster than the conventional EX-algorithm for circuits with the similar gate sizes. Experimental results have shown that the algorithm locates all errors at high hit ratio for ISCAS benchmark circuits and some other circuits.

This paper presents an efficient heuristic algorithm for min-cut bisection of weighted hypergraphs. The proposed algorithm is based on a heuristic algorithm proposed by Kahng, which was devised for non-weighted hypergraph bisection, adopting a non-weighted graph called intersection graph to represent a given hypergraph. In the proposed algorithm, instead of an intersection graph, a bipartite graph called netgraph is newly introduced to explicitly represent the weights of nodes of a hypergraph. Using the netgraph, it is easy to partition a weighted hypergraph into two hypergraphs with same size. Computation time of the proposed method is O(m²), where m is the number of nodes of a given hypergraph. Experimental results with real circuit data show that the proposed method produces better solutions in shorter computation time compared with existing methods.

A new algorithm for timing driven placement based on the fuzzy theory is proposed. In this method, the signal delay on the longest path, the chip area and the total wire length can be simultaneously minimized. Introducing the probability measures of fuzzy events, falling down into the local optimal solutions can be avoided. At first, we define the fuzzy placement relation using the graph distance matrix and fuzzy distance relation matrix, and we give a new placement method based on the fuzzy placement relation and the probability measures of fuzzy events. Secondly, we extend this placement method so as to apply to the timing driven placement problem by introducing a fuzzy membership functions which represent the signal delay on the longest path and the chip area. Finally, experimental results are shown to compare our method with one of the previous methods.

This paper deals with the sub-problems of generating a mask pattern from the logical description of a large-scale CMOS circuit. The large-scale layout can be generated in divide-and-conquer style: divide a given circuit into a set of sub-circuits, generate the layout of each sub-circuit, and merge the resulting layouts to create the whole layout. This paper proposes a layout synthesis algorithm for a sub-circuit with physical constraints for the synthesis scheme above. The physical constraints considered here are the relative placement of logic cells (sets of logic gates) and the routing constraint based on the costs of wiring layers and vias. These constraints will be given by the global optimizer in a two-dimensional layout synthesis routine, and they should be kept at the subsequent one-dimensional layout synthesis for a sub-circuit. The latter is also given for enhancing the circuit performance by limiting the usage of wiring layers and vias for special net such as a clock net. The placement constraint is maintained using PQ-tree, a tree structure representing a set of restricted permutations of elements. One-dimensional layout synthesis determines the placement of transistors by the enhanced pairwise exchanging method under the PQ-tree representation. The routing constraints is considered in the newly developed line-search routing method using a cost-based searching. Experimental results for practical standard cells, including up to 200 transistors, prove that the algorithms can produce the layouts comparable to handcrafted cells. Also on a two-dimensional layout synthesis using the algorithms, the results for benchmark circuits of Physical Design Workshop 1989, i.e., MCNC benchmark circuits, are superior to the best results exhibited at Design Automation Conference 1990.

We propose a hierarchical multi-layer global router for Sea-Of-Gates VLSI's, which is different from the conventional global routers, in that routing and layering are executed simultaneously. The main problems to be solved in the global routing for a multi-layer VLSI are which wire segments are laid out on upper layers and how they are connected to terminals located on lower layers. The main objective is to minimize the maximum of local congestions of all layers. We solve these problems in a hierarchical manner by routing from upper layers to lower layers.

An automatic macrocell generator has been developed and applied to the analog layout of SC and active-RC filters. The generator consists of a process independent generation procedure, a leafcell library, and a circuit description of the leafcells. The unit element arrays of the whole filter are generated together to minimize the array height of the entire filter macrocell, so that the area of the generated filter is as small as that of a manually laid out filter. Three SC filters and one active-RC filter were designed and fabricated by 1.5-µm CMOS technology, that successfully yielded an S/N ratio of more than 70 dB with a quick turn around time.

An autonatic layout scheme dedicated to bipolar analog modules is described. A layout model is settled in such a way that the V_CC/G_ND line is laid out on top/bottom edge of a rectangular region, within which the whole elements are placed and interconnected. According to this simple modeling, a layout scheme can be constructed of a series of the following algorithms: First clustering is executed for partitioning a given circuit into clusters, each having connections with V_CC and G_ND lines, and then linear ordering is applied to clusters so as to be placed in a one-dimensional array. After a relative placement of circuits elements in each cluster, a block compactor is implemented by means of packing blocks in each cluster into an idle space, and then a detailed router is conducted to attain 100% interconnection. Finally a layout compactor is invoked to pack all layout patterns into a rectangle of the minimum possible area. A number of implementation results are also shown to reveal the practicability of the proposed analog module generator.

Net-Oriented Analysis and Design (NOAD) is defined as three items: (1) Various nets are utilized as an effective modeling method. (2) Inter-relationships among verious nets are determined. (3) Verification or analysis methods for nets are provided and they are implemented based on the mathematical theory, that is Net theory. Very few methods have been presented to satisfy these three items. For example, the Real-Time SA method covers item (1) only. The Object-Oriented Analysis and Design method (OOA/OOD) covers items (1) and (2). NOAD can be regarded as an extension to OOA/OOD. This paper discusses how effectively various nets have been used in actual software development support metnods and tools and evaluates such several methods and tools from the NOAD viewpoint.

This paper describes a programming system, K-NET for the development of control software for flexible manufacturing systems composed of robots, numerically-controlled machines, transfer machines and automatic storage/retrieval systems. K-NET is based on a high-level Petri net which makes it simple to express operational functions such as synchronization, interlock and concurrence in sequence control. Petri net in K-NET is colored one in which tokens have attributes, and timed one which can provide a notion of stochastic time. K-NET provides many kinds of boxes having specific functions, and gates specified the firing condition and the token flow control with IF-THEN rules. On the other hand, procedural language can be also used for information processing. K-NET can support all development stages including general design, detailed design, programming and testing. K-NET has an editor to input control specifications expressed with Petri net; a simulator to verify edited specifications; a generator to convert the net to C source programs for a computer or to ladder diagrams for a programmable controller; a reporter to print control specifications; and a monitor to display controller status in real-time. K-NET has been used in the development of control software for an automated guided vehicle system, and results show a 2/3rds cost-saving over development with conventional methods in which only procedural language is used.

This paper describes MENDELS ZONE, a Petri-net-based concurrent programming environment, which is especially suitable for cooperating discrete event systems. MENDELS ZONE adopts MENDEL net, which is a type of high level (hierarchical colored) Petri net. One of the characteristics of the MENDEL nets is a process-oriented hierarchy like CCS, which is different from the subnet-oriented hierarchy in the Jensen's hierarchical colored Petri net. In a process-oriented hierarchy, a hierarchical unit is a process, which is more natural for cooperating and decentralized discrete event control systems. This paper also proposes a design methodology for MENDEL nets. Although many Petri net tools have been proposed, most tools support only drawing, simulation, and analysis of Petri nets; few tools support the design methodology for Petri nets. While Petri nets are good final design documents easy to understand, analyzable, and executable it is often difficult to write Petri nets directly in an earlier design phase when the system structure is obscure. A proposed design methodology makes a designer to construct MENDEL nets systematically using causality matrices and temporal logic. Furthemore, constructed MENDEL nets can be automatically compiled into a concurrent programming language and executed on a parallel computer.

An integrated platform INTEGRAL has been developed for developing large complex communication software systems. At the heart of INTEGRAL, a pair of graphical and textual specification languages, DISCOL (DIStributed Communication-Oriented Language), has been developed based on Petri nets. Around DISCOL, a wide variety of design and analysis tools have been integrated in coherent manner so that a seamless support from design to verification and testing are made available along with software life-cycle. The platform has been applied to the development of a PBX simulator named UICPBX. In the development, some real communication services have been fully specified with DISCOL. Such experiences have revealed the effectiveness of the proposed techniques.

Recent trends in down-sizing have resulted in the development of client server systems for many industries. This paper considers the application of stochastic Petri nets with general firing times for modeling of a concatenated client server system and the use of discrete-event simulation methods for stochastic Petri nets to study its behavior. This approach enables us to assess the most appropriate resource set of a concatenated client server system on the quantitative basis of the performability and the occurrence of system down conditions. Thus, system consultation, a new application of stochastic Petri nets, is presented.

The pursuit of higher availability has resulted in the development of fault tolerant systems for many industries. However, system characteristics that can be perceived by the customer have never been diagnosed quantitatively. This paper considers the application of stochastic Petri nets with general firing times to modeling of a fault tolerant system and the use of discrete-event simulation methods for stochastic Petri nets to study the behavior of the system. The stochastic Petri net model incorporates factors that compose the system as well as those that accompany it, including RAS characteristics of products, personnel arrangements, and system management. By modeling the behavioral aspect of each factor, it is possible to diagnose a fault tolerant system quantitatively on the basis of customer impact.

Stochastic Petri Nets and Generalized Stochastic Petri Nets as well as other extensions to Stochastic Petri Nets have been widely applied as a model of asynchronous concurrent process, or as an aid to analyze or design concurrent systems. This paper presents an Extended Stochastic Petri Net model for a shift processing system in which three kinds of sink may occur and an arbitrary time distribution is incorporated, provides an analytical method based on a Markov renewal process with some non-regeneration points to clarify the probabilistic behavior of the system, and finally evaluates the performance of the system with numerical values.

A job shop system typically seen in flexible manufacturing systems (FMS) is a system composed of a set of machines and a various kind of jobs processed with the machines. A production system of semiconductor fabrication is an example of job shop systems, which has main features of repetitive processes of one part and set-up times required for machines processing different types of parts. On the other hand, timed Petri nets are used for modelling and analyzing a wide variety of discrete event systems. There are many applications of timed Petri nets to the scheduling problems of job shop systems. The performance evaluation and steady state behaviors are studied by using the maximum cycle time of timed marked graphs. The aim of this paper is to propose a new model for production systems including repetitive processes and set-up time requirements which enables the quantitative analysis of real time system performance. In job shop systems such as a semiconductor fabrication system, it takes considerable amount of set-up time to prepare different types of chemical reactions and the model should take account of a set-up time for each machine. We focus upon the relationship between facility utilization factor and production cycle time in the steady state. In the proposed model, the minimum total set-up time can be attained. Quantitative relationship between utilization factor and production cycle time is derived by using the proposed model. A utilization factor of a system satisfying a given limit of the cycle time is evaluated, and the improvement of the utilization factor is considered. Conversely, we consider the improvement of the cycle time of a system satisfying a given limit of utilization factor.

The subject of the paper is to propose two approximation algorithms FM_SPLA, FM_DPLA for priority-list scheduling in timed Petri nets. Their capability is compared with that of existing algorithms SPLA, DPLA through experimental results, where SPLA and DPLA have previously been proposed by the authors.

The subject of the paper is the minimum initial marking problem for scheduling in timed Petri net PN: given a vector X of nonnegative integers, a P-invariant Y of PN and a nonnegative integer π, find an initial marking M minimizing the value Y^tr・M among those initial marking M such that there is a scheduling σ having the total completion time τ(σ)π with respect M , X and PN (a sequence of transitions, with the first transition firable on M , such that every transition t can fire prescribed number X(t) of times). The paper shows NP-hardness of the problem and proposes two approximation algorithms with their experimental evaluation.

This paper describes a modeling of the cryptography based on a concept of Petri nets. Movement of tokens in the net model shows a dynamic behavior of systems. On the other hand, the cryptography is considered as a bit operation, so that we can point out a common property between the net structure and the cryptography, which provides our idea that movement of tokens of the net model corresponds to a bitoperation of the cryptography. Some effective keys in the net model are considered by means of the net elements, which are based on T-invariant and net structures. It is shown that the keys of the net structured cryptography provide reasonable strength comparing with the data encryption standard (DES).

In most of the methods proposed so far to design approximately linear phase IIR digital filters (IIR DFs), the design takes place only in the time or in the frequency domain. However, when both magnitude and phase responses are considered, IIR DFs with better frequency responses can be obtained if their characteristics in both domains are taken into account. This paper proposes a design method for approximately linear phase IIR DFs, which is based on parameter estimation techniques in the time domain followed by a nonlinear optimization algorithm in the frequency domain. Several examples are presented, illustrating the proposed method.

OGIS Research Institute and Osaka Gas have developed two intelligent tutoring systems (ITSs): PCTS (Process Control Training System) and PDTS (Power Distribution Training System). This paper describes a basic concept of an ITS for plant operation based on the experience of their development. The topics include: (1) The features and structure of PCTS (i.e., text based training and model based training, a simulation model based on OOP, an intelligent authoring system). (2) What kinds of stages are needed for training systems from the view point of cognitive science (i.e., verbal learning multiple discrimination learning, rule learning, compound rule learning problem solving). (3) How to detect trainees' missing operational steps and misoperations using the perturbation method.