G.D. Hachtel and F. Somenzi. Logic synthesis and verification algorithms. Kluwer Academic Publishers, Boston, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....cofactor) is = 021 3 545454 5 A 545454 ;1 . The cofactor of with respect to variable 1: the negative cofactor) is = B 021 3 54 4545 C# 454545 1 6 . The Boole s expansion of a function over a variable (also called Shannon s expansion) is given as follows [22] [23]: Let D)E . Then, 021 3 1F9 545454 1 454545 1 G6 H1: F = I 1 J = Let and be two functions with support variables 1: L NM 454545 8 O be an arbitrary binary operator, representing a Boolean function of two arguments. The orthonormal ....

.... G6 H1: F = I 1 J = Let and be two functions with support variables 1: L NM 454545 8 O be an arbitrary binary operator, representing a Boolean function of two arguments. The orthonormal expansion of OPK with respect to is given as [24] [23]: QOHKR S1 0T = O K = 6 1G N0T = O K = VU:L A M# 454 45 8 A function can be represented as a sum of products of literals, called the minterms of the function. Operations on Boolean functions over the same domain can be viewed as operations on the set of their minterms. ....

G.D. Hachtel and F. Somenzi, Logic Synthesis and Verification Algorithms, Kluwer Academic Publishers, 1996.

....we can usually make a circuit smaller if we apply our complex transformation to appropriate portions of the circuit. To find the best portion to which we should apply the transformation is a combinatorial problem similar to finding a best divisor in the conventional multilevel logic synthesis [7]. 6. CONCLUDING REMARKS As mentioned earlier, our ultimate goal is to develop a design theory for quantum Boolean circuits. For this purpose: 1) We will need more concrete guide or heuristics on how to change a given circuit into a better circuit. 2) During the course of this research, we ....

G. D. Hactel and F. Somenzi. Logic Synthesis and Verification Algorithms. Kluwer Academic Publishers, 1996.

....activatable clusters. An elementary clusteractivation ecs is a set ecs = # i # act , where exactly one cluster is selected per activated interface. Since every activatable cluster has to be part of the implementation to obtain the expected flexibility, we have to determine a coverage [5] of # act by elementary cluster activations. As example consider Figure 2. For a given resource allocation PC 2 A, the clusters # D1 , # D2 , # U1 , and # U2 are activatable. One coverage of this set is given by the elementary cluster activations # U1 and D1 #U2 . Given an elementary ....

....graph. Finally, we validate all timing constraints that are imposed on our implementation. Here, we use a statistical analysis method to check for fulfillment. With these basic ideas of pruning the search space, we formulate our exploration algorithm based on a branch and bound strategy [5, 8]. For the sake of clarity, we omit details for calculating a coverage of activatable problem graph clusters or successive flexibility estimation, etc. The following code should be self explanatory with the previous comments. EXPLORE IN: specification graph G S OUT: Pareto optimal set BEGIN ....

G. D. Hachtel and F. Somenzi. Logic Synthesis and Verification Algorithms. Kluwer Academic Publishers, Norwell, Massachusetts 02061.

....systematic Boolean minimization methods mostly copy the structure of the original method by Quine and McCluskey [Qui52, McC56] implementing the two basic phases known as prime implicant (PI) generation and covering problem (CP) solution. Some more modern methods, including the well known ESPRESSO [Bra84, Hac96], try to combine these two phases and thus all the PIs need not be evaluated. One of the most successful Boolean minimization methods is ESPRESSO and its later improvements. The original ESPRESSO generates near minimal solutions, ESPRESSO EXACT [Rud87] was developed in order to improve the ....

Hachtel, G.D - Somenzi, F.: Logic synthesis and verification algorithms, Boston, MA, Kluwer Academic Publishers, 1996, 564 pp.

.... , the dual Kripke structure K(q; Y; Z ; Z ) is obtained from K by dualizing the value of q in states in Y , adding to R transitions in Z , and removing from R 3 The logic based de nition of coverage is closely related to the notion of observability don t care conditions as presented in [HS96]. There, there is a set C 0 C of control signals and an assignment : C 0 ftrue; falseg for the signals in C 0 , such that the behavior of all states of the system that agree with about the assignment to the control signals in C 0 is the same (in terms of the assignment to the ....

G.D. Hachtel and F. Somenzi. Logic Synthesis and Verication Algorithms. Kluwer Academic Publishers, Norwell, Massachusetts, 1996.

....order to support identification of the design origin and the original recipient. Combinational logic synthesis has been thoroughly studied. Detailed description of optimization problems and a good survey of minimization techniques and existing non commercial synthesis frameworks is presented in [Mic94, Hac96]. The targets of latest improvements in combinational logic synthesis are refined covering algorithms [Cou92, Lia97, Gol97] optimizations on networks described using black boxes [Liu97] power optimization [Nar97, Tiw96] etc. Similarly, the research activity in technology mapping has been ....

....a given library, the goal of a multi level logic minimization strategy is to find an equivalent quasi alternate multilevel representation of the input for which the set of targeted design properties is optimal. A good survey of optimization strategies for multi level logic minimization is given in [Mic94, Hac96]. 3.2. Technology mapping (cell library binding) In this step of logic synthesis, the output of the multi level logic minimization (a logic network) is mapped to a predefined cell library or a network of lookup tables (LUTs) The mapping is performed in a way that the original network is ....

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G.D. Hachtel and F. Somenzi. Logic synthesis and verification algorithms. Kluwer Academic Publishers, Boston, 1996.

....by Quine [11] and McCluskey [8] which formed a basis for many follow up methods. These mostly copied the structure of the original method, implementing the basic two phases known as PI generation and covering problem (CP) solution. Some more modern methods, including the well known ESPRESSO [15] [6] with its later improvements ESPRESSO EXACT and ESPRESSO SIGNATURE [9] combine these two phases, reducing the number of implicants to be processed. A sort of combination of PI generation with solution of the CP, leading to a reduction in the total number of prime implicants generated, is also ....

.... suggested in [13] 3] For multi output functions there is on top of that an Implicant Reduction phase, which derives group implicants from PIs and finally the Output Reduction, which eliminates redundant implicants of individual outputs (corresponding to the ESPRESSO s MAKE SPARSE procedure [6]) 3.1 Mutations The heuristics used to implement individual steps of this procedure are based on the study of statistical properties of the given Boolean functions. The results of these tests often give results whose interpretation is not straightforward and thus several different decisions may ....

Hachtel, G.D. - Somenzi, F.: Logic synthesis and verification algorithms. Boston, MA, Kluwer Academic Publishers, 1996, 564 pp.

....means, e.g. combining PI generation with the solution of the covering problem (CP) in order to reduce the size of the problem and above all to reduce the number of implicants to be processed. This combination is a characteristic feature of several modern methods, including the well known ESPRESSO [4, 7] with its later improvements ESPRESSO EXACT and ESPRESSOSIGNATURE [9] This approach is used also in BOOM, namely in the primary implicant generation phase the coveragedirected search . A common feature of all methods proposed so far is obtaining the final solution from an initial solution ....

....in Section 4. The results of extensive experimental verification are evaluated and commented in Section 5, and the time complexity of the proposed algorithm is evaluated in Section 6. 2. The Problem of Boolean Minimization The problem of two level minimization will be defined in a usual way [4, 6, 7]. A Boolean function of n input variables is defined by a truth table describing the on set F(x 1 , x 2 , x n ) and off set R(x 1 , x 2 , x n ) Here the on set (off set) is the set of terms to which the output value 1 (0) is assigned. Both minterms and terms of higher dimension may be ....

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Hachtel, G.D. - Somenzi, F.: Logic synthesis and verification algorithms. Boston, MA, Kluwer Academic Publishers, 1996, 564 pp.

....able to cope with the existence of large number of prime implicants (PIs) of the given function, while most of them are not needed for the minimal solution. There are scores of texts treating the problem of Boolean minimization, hence it is impossible even to mention them. Some books like e.g. [1, 6] give a good survey of the important methods and their lists of references can be used as pointers to most of the important papers. Although these methods differ in many practical aspects, they mostly preserve the main feature of the original method, namely the use of two basic phases known as PI ....

....of the important papers. Although these methods differ in many practical aspects, they mostly preserve the main feature of the original method, namely the use of two basic phases known as PI generation and covering problem (CP) solution. Some more modern methods, including the well known ESPRESSO [1, 6] with its later improvements ESPRESSO EXACT and ESPRESSO SIGNATURE [9] combine these two phases, reducing the number of implicants to be processed. A sort of combination of PI generation with the solution of the CP, leading to a reduction in the total number of prime implicants generated, is ....

[Article contains additional citation context not shown here]

Hachtel, G.D. - Somenzi, F.: Logic synthesis and verification algorithms. Boston, MA, Kluwer Academic Publishers, 1996, 564 pp.

....a natural hierarchy is formed. For the second input, each of the tasks within a composite task is assigned expected sequential behaviors from the sequential library. These are nondeterministic finite automata, NFA, represented implicitly with Reduced Ordered Binary Decision Diagrams, ROBDDs [16][48][90] 93] These NFA, called modeling automaton, MA, encapsulate anticipated sequential behaviors for targeted low level hardware units. Additional sequential constraints, such as protocols, drawn from the sequential library, may also be included as input. The final and third input is resource ....

....Its purpose is to highlight what is at the core of ABSS models while ignoring, for now, other important considerations such as protocols and control dependent behavior. In practice, all ABSS models are implicitly and efficiently represented with Reduced Ordered Binary Decision Diagrams, ROBDDs [16][48][90] 93] Figure 2.3 Example looping behavioral description rv2 = 0; while (TRUE) i0 = read( i1 = read( i2 = read( rv0 = i0 i1; Task v0 rv1 = rv0 rv2; Task v1 19 Figure 2.3 is a looping pseudocode behavioral description which may be cast as a scheduling problem. For ....

G. Hachtel and F. Somenzi, Logic Synthesis and Verification Algorithms, Kluwer Academic Publishers, 1996.

....[Qui52] which formed a basis for many follow up methods. They mostly copied the structure of the original method, implementing the two basic phases known as prime implicant (PI) generation and covering problem (CP) solution. Some more modern methods, including the well known ESPRESSO [Esp1] [Hac96], try to combine these two phases. This is motivated above all by the fact that the problems encountered in modern application areas like design of control systems, design of built in self test equipment, etc. often require minimization of functions with hundreds of input variables, where the ....

Hachtel, G.D. - Somenzi, F.: Logic synthesis and verification algorithms. Boston, MA, Kluwer Academic Publishers, 1996, 564 pp.

....software engineering, etc. The minimization methods started with the papers by Quine and McCluskey [6] 9] which formed the basic two phases known as prime implicant (PI) generation and covering problem (CP) solution. Some more modern methods, including the well known ESPRESSO [13] [4] try to combine these. This is motivated above all by the fact that the problems encountered in modern application areas like design of control systems, design of built in self test equipment, etc. often require minimization of functions with hundreds of input variables, where the number of PIs ....

....functions. However, to obtain the minimal solution, we may need implicants of more than one output function that are not primes of any. Here, Implicant Reduction takes place. Then the Group Covering Problem is solved and Output Reduction (corresponding to the ESPRESSO s MAKE SPARSE procedure [4]) is performed. 3.2 Iterative Minimization Most current heuristic Boolean minimization tools, including ESPRESSO, use deterministic algorithms. Here the minimization process always leads to the same solution, never mind how many times it is repeated. On the contrary, in the BOOM system the ....

Hachtel, G.D. - Somenzi, F.: Logic synthesis and verification algorithms. Boston, MA, Kluwer Academic Publishers, 1996, 564 pp.

....circuit behavior (see e.g. 1] So far, several verification approaches for SystemC have been reported, but all of them are based on simulation [10, 6] and do not consider the paradigms of formal techniques, i.e. to prove the correctness of a circuit behavior. As has been observed by many authors [5, 3, 7, 4, 13, 8], formal verification is very closely related to reachability analysis of Finite State Machines (FSMs) if the underlying circuit is modeled appropriately. This directly results from This work was supported in part by DFG grant DR 287 8 1. the fact that for each state in the circuit it has to ....

G. Hachtel and F. Somenzi. Logic Synthesis and Verification Algorithms. Kluwer Academic Publisher, 1996.

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G.D. Hachtel and F. Somenzi. Logic synthesis and verification algorithms. Kluwer Academic Publishers, Boston, 1996.

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G.D.Hachtel and F. Somenzi, Logic synthesis and verification algorithms. Boston, MA, Kluwer Academic Publishers, 1996, 564 pp.

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Hachtel, G. D.---Somenzi, F.: Logic Synthesis and Verification Algorithms. Boston, MA, Kluwer Academic Publishers, 1996, pp. 564.

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HACHTEL, G.D. - SOMENZI, F.: Logic synthesis and verification algorithms. Boston, MA, Kluwer Academic Publishers, 1996, 564 pp.

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HACHTEL, G.D. - SOMENZI, F.: Logic synthesis and verification algorithms. Boston, MA, Kluwer Academic Publishers, 1996, 564 pp.

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G. D. Hachtel, and F. Somenzi, Logic synthesis and verification algorithms. Kluwer Academic Publishers, Norwell, MA, 1996.

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Gary D. Hachtel and Fabio Somenzi. Logic Synthesis and Verification Algorithms. Kluwer Academic Publishers, Boston, May 1996.

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Hachtel, G.D., Somenzi, F.: Logic Synthesis and Verification Algorithms. 2 edn. Kluwer Academic Publishers, Norwell, Massachusetts 02061 USA (1998)

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G. Hachtel and F. Somenzi. Logic Synthesis and Verification Algorithms. Kluwer Academic Publishers, 1996.

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Gary Hachtel and Fabio Somenzi. Logic Synthesis and Verication Algorithms. Kluwer Academic Publishers, 1996.

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G. D. Hachtel and F. Somenzi, Logic Synthesis and Verification Algorithm, Kluwer Academic Publishers, 1996

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G. D. Hachtel and F.Somenzi, Logic Synthesis and Verification Algorithms,Kluwer Academic Publishers, June 1996.

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