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On the complexity of classification functions
 in ISMVL
, 2008
"... A classification function is a multiplevalued input function specified by a set of rules, where each rule is a conjunction of range functions. The function is useful for packet classification for internet, network intrusion detection system, etc. This paper considers the complexity of range func ..."
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A classification function is a multiplevalued input function specified by a set of rules, where each rule is a conjunction of range functions. The function is useful for packet classification for internet, network intrusion detection system, etc. This paper considers the complexity of range functions and classification functions represented by sumofproducts expressions of binary variables. It gives tighter upper bounds on the number of products for range functions. 1.
Largescale SOP minimization using decomposition and functional properties
 40th Design Automation Conference, Ahaneim
"... In some cases, minimum SumOfProducts (SOP) expressions of Boolean functions can be derived by detecting decomposition and observing the functional properties such as unateness, instead of applying the classical minimization algorithms. This paper presents a systematic study of such situations and ..."
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In some cases, minimum SumOfProducts (SOP) expressions of Boolean functions can be derived by detecting decomposition and observing the functional properties such as unateness, instead of applying the classical minimization algorithms. This paper presents a systematic study of such situations and develops a divideandconquer algorithm for SOP minimization, which can dramatically reduce the computational effort, without sacrificing the minimality of the solutions. The algorithm is used as a preprocessor to a generalpurpose exact or heuristic minimizer, such as ESPRESSO. The experimental results show significant improvements in runtime. The exact solutions for some large MCNC benchmark functions are reported for the first time.
GPU Acceleration of NearMinimal Logic Minimization
"... Abstract—In this paper, we describe a GPUaccelerated implementation of a logic minimization heuristic based on the near minimal approach. This algorithm has three key kernel computations, and the current version of our implementation, we adapted one of these kernels for GPU execution. In this paper ..."
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Abstract—In this paper, we describe a GPUaccelerated implementation of a logic minimization heuristic based on the near minimal approach. This algorithm has three key kernel computations, and the current version of our implementation, we adapted one of these kernels for GPU execution. In this paper we report our results gained from using NVIDIA’s CUDA development framework and an NVIDIA Tesla GPUs, achieving a nearly 10X speedup as compared to a software implementation executed on a Xeon 5500series processor.
Prime and Essential Prime Implicants of Boolean Functions through Cubical Representation
"... K Maps are generally and ideally, thought to be simplest form for obtaining solution of Boolean equations.Cubical Representation of Boolean equations is an alternate pick to incur a solution, otherwise to be meted out with Truth Tables, Boolean Laws and different traits of Karnaugh Maps. Largest pos ..."
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K Maps are generally and ideally, thought to be simplest form for obtaining solution of Boolean equations.Cubical Representation of Boolean equations is an alternate pick to incur a solution, otherwise to be meted out with Truth Tables, Boolean Laws and different traits of Karnaugh Maps. Largest possible k cubes that exist for a given function are equivalent to its prime implicants. A technique of minimization of Logic functions is tried to be achieved through cubical methods. The main purpose is to make aware and utilise the advantages of cubical techniques in minimization of Logic functions. All this is done with an aim to achieve minimal cost solution.
A Novel Essential Prime Implicant Identification Method for Exact Direct Cover Logic Minimization
"... Abstract Most of the directcover Boolean minimization techniques use a four step cyclic algorithm. First, the algorithm chooses an Onminterm; second, it generates the set of prime implicants that covers the chosen minterm; third, it identifies the essential prime implicant; and fourth, it perform ..."
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Abstract Most of the directcover Boolean minimization techniques use a four step cyclic algorithm. First, the algorithm chooses an Onminterm; second, it generates the set of prime implicants that covers the chosen minterm; third, it identifies the essential prime implicant; and fourth, it performs a covering operation. In this study, we focus on the third step and propose a new essential prime implicant identification method. In this method, when the identification of the essential prime implicant is impossible, we postpone dealing with current Onminterm and save a status word for it. Eventually, we retrieve the status words whenever a new essential prime implicant is identified. We compared the proposed minimization method with ESPRESSOEXACT. The results show that our method obtains exact results faster than other ones.
A NEW METHOD BASED ON CUBE ALGEBRA FOR THE SIMPLIFICATION OF LOGIC FUNCTIONS
"... In this study an Offset based directcover minimization method for singleoutput logic functions is proposed represented in a sumofproducts form. To find the sufficient set of prime implicants including the given Oncube with the existing directcover minimization methods, this cube is expanded f ..."
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In this study an Offset based directcover minimization method for singleoutput logic functions is proposed represented in a sumofproducts form. To find the sufficient set of prime implicants including the given Oncube with the existing directcover minimization methods, this cube is expanded for one coordinate at a time. The correctness of each expansion is controlled by the way in which the cube being expanded intersects with all of K<2 n Offcubes. If we take into consideration that the expanding of one cube has a polynomial complexity, then the total complexity of this approach can be expressed as O(n p)O(2 n), that is, the product of