Figure 3
![Polymorphic even/odd parity circuit created by means of constructor [MODIS 4 3] [MODFS 13 17] [CPMIS 0 1] [MODIS 0 2] [CPOS 3 1] (a 5- instruction constructor, even number of inputs)](profile/Lukas_Sekanina/publication/220743545/figure/fig1/AS:305413221306370@1449827594964/Polymorphic-even-odd-parity-circuit-created-by-means-of-constructor-MODIS-4-3-MODFS-13.png)
Polymorphic even/odd parity circuit created by means of constructor [MODIS 4 3] [MODFS 13 17] [CPMIS 0 1] [MODIS 0 2] [CPOS 3 1] (a 5- instruction constructor, even number of inputs)
Source publication
This paper deals with the evolutionary design of programs (constructors) that are able to create (n+2)-input circuits from n-input circuits. The growing circuits are composed of polymorphic gates considered as building blocks. Therefore, the growing circuit can specialize its functionality according to environment which is sensed through polymorphi...
Context in source publication
Context 1
... structure is not surprising; however, the structure was designed fully automatically without any supporting domain knowledge (we started with the empty embryo (0, 0, I/I, I/I)). Figures 3 and 4 show two poly- morphic circuits calculating even/odd parity functions. We have gained 35 general constructors out of 200 independent runs of the evolutionary design process for a five-instruction chromosome. ...
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Citations
... For example, a AND/OR gate controlled by VDD was designed in [1], and a NAND/NOR gate fabricated in a 0.7 μm CMOS was reported in [5]. Evolutionary Algorithms (EAs) have been adopted to design polymorphic circuits [4,[6][7][8][9][10]. In [9], a circuit which operates as a 3×4 multiplier in mode 1 and as a 7-bit sorting net in mode 2 was evolved, and it is the largest polymorphic circuit that has ever been generated. ...
Polymorphic circuits are a special kind of circuits which possess some different build-in functions and these functions are activated by environment parameters, like light and VDD. Some theories have been proposed to guide the design of polymorphic circuits, including the definition of complete polymorphic gate sets and algorithms to judge the completeness of a polymorphic gate set. However, the previous algorithms have to enumerate all the polymorphic signals for judging the completeness of a polymorphic gate set, and it is not easy to be conducted manually. In this paper, a straightforward method is proposed to judge the completeness of a polymorphic gate set. And the correctness of the straightforward method is proved theoretically. Some examples are given to show that the proposed method could be conducted step by step. Its actual computing cost is usually low, and it is suitable for manual operation.
... connection of components) is fixed; however, the components can change the functionality. In other approach, Bidlo et al. applied an instruction-based development for the evolutionary design of arbitrarily large polymorphic sorting networks [9]. The polymorphic sorting networks are able to sort the input sequences into the nondecreasing order in environment E1 and into the non-increasing order in environment E2. ...
Cellular automata-based evolutionary development is pre- sented for the design of single-function and polymorphic (two-function) combinational circuits. The impact of evolution of the cellular automaton initial state on the success rate of the evolved solutions is investigated. The experiments show that it is more suitable to fix a proper initial state in order to increase the successfulness and speed of evolution. The pro- posed developmental model is capable to design a wide range of both single-function and polymorphic circuits.
... The other research group in this field is led by Sekanina. Sekanina et al. [8,[12][13][14] evolved the gate-level polymorphic digital circuits using polymorphic gates as building blocks and discussed the scalability problem of the polymorphic digital circuit design. Based on the basic polymorphic gates implemented by Stoica and coworkers, Sekanina et al. [14] also did some work on the improvement of existing polymorphic gates in order to design nontrivial multifunctional circuits controlled by Vdd. ...
A general design approach to design polymorphic circuits with polymorphic gates is proposed. These polymorphic circuits can adaptively adjust their functionalities with the changes of the electrical characteristics of components induced by the change of environment. The single function circuits that can work correctly and maintain their functionalities in different environments can be regarded as a special kind of polymorphic circuits. The general design approach for these circuits is proposed, and based on this approach, the general design approach to designing polymorphic circuits is also proposed. It is proved that a polymorphic circuit with any two different functions in two different environments can be implemented with a complete polymorphic gate set, and a definition on the gate set is given and the completeness is also discussed. Finally, these general design approaches are analysed and some experiments are performed to demonstrate their efficiency.
... However, polymorphic circuit can not be designed with conventional methods, and it is difficult to evolve polymorphic circuit with evolutionary algorithms directly. Sekanina and his colleagues have adopted evolutionary algorithms to design some small scale polymorphic circuits at gate level678910. The most complex circuit evolved has up to 6 inputs and 6 outputs, and consists of several tens of gates [10]. ...
Polymorphic circuit is a kind of multifunctional circuits that can perform two or more functions under different conditions.
And those functions can be activated by changing control parameters, such as temperature, power supply voltage, illumination
and so on. Polymorphic circuit provides a novel approach to build multifunctional circuits, and it can be used in many fields.
However, polymorphic circuit can not be designed with conventional methods and is hard to be evolved with evolutionary algorithms
directly. A novel evolutionary algorithm based on the weighted sum method is proposed in this paper, which can be used to
evolve polymorphic circuits at gate level. The experimental results demonstrate that this algorithm can increase the success
ratio and decrease the evolutionary generations needed to evolve a polymorphic circuit.
... The goal of this paper is to utilize an artificial developmental model based on application-specific instructions in connection with the genetic algorithm in order to (1) reduce the length of the chromosome needed for encoding the target circuits, (2) introduce an external control of the developmental process in form of a string of values interpreted as a biologically inspired environment for the construction of irregular structures, (3) enable to design generic combinational multipliers and (4) demonstrate the ability of the system to adapt to different environments retaining the capability to design generic structures. A concept of environment was proposed in [3], where the environment was utilized to affect the function of polymorphic circuits [1]. In this paper the environment is intended to influence the development of the circuit structure. ...
A system is presented utilizing a simple genetic algorithm combined with a developmental model for the evolutionary design of generic structures of combinational multipliers. An artificial environment is introduced into the system interpreted as an external control of the developmental process allowing to design irregular structures (inspired by the irregularity observed in conventional multipliers). Two sorts of experiments were conducted in order to demonstrate the ability of the system to adapt to different environments. The approach presented in this paper poses the first case in the field of the evolutionary design when generic multipliers have been evolved by means of the development.
... In the cases it did, it re-lied for publication not only on the result, but also on the technique. The work of Stoica with polymorphic circuits [28] demonstrated the invention of a new class of circuits, however search for a good application for such functionality is still on [6]. Aggarwal's work was concentrated on evolution of sine-wave oscillators. ...
Our interest is in evolutionary electronics and its exploitation for invention. In this paper, we survey how the community currently tries to exploit the invention potential of evolvable hardware. We assess whether the current state-of-art in evolvable hardware has resulted in successful inventions or invention tools. We discuss the challenges faced by the community in this regard and how the community can overcome these challenges by exploiting nascent technologies, which include new design substrates, new computational paradigms and recently discovered design principles
... Some of them have been fabricated and evaluated in a real environment [8]. In another research [6, 5, 1], multifunctional combinational modules composed of polymorphic gates were designed by means of evolutionary techniques. The resulting circuits are composed of standard as well as polymorphic gates and exhibit various unusual functions, for example, one of these circuits could operate as a two-bit adder when Vdd is 3.3V and as a two-bit multiplier when Vdd is 1.2V. ...
Polymorphic electronics provides a new way for obtaining circuits that are able to perform two or more functions depending on the environment in which they operate. These functions can be activated under certain conditions by changing control parameters of the circuit (such as temperature, power supply voltage, light etc.). Existing polymorphic gates are difficult to use as building blocks in complex digital circuits. In this paper, some modifications of existing polymorphic gates are proposed in order to utilize them in non-trivial digital multifunctional circuits. The presented multifunctional circuits composed of these gates represent the most complex multifunctional circuits available nowadays. In particular, NAND/NOR and AND/OR polymorphic gates controlled by the power supply voltage are discussed and used in circuits such as the five-bit majority/ AND circuit and three-bit multiplier/six-bit sorting network circuit.
... In fact, the presented system was able to design a wide variety of structures of growing sorting networks [7]. Moreover, polymorphic 1 sorting networks have been discovered which sorts the input sequence into the non-decreasing order in one mode and into the non-increasing order in another mode [11]. In the next section, we focus on analyzing the best evolved constructor presented herein. ...
A method is presented for the construction of arbitrary even-input sorting networks exhibiting better properties than the networks created using a conventional technique of the same type. The method was discovered by means of a genetic algorithm com-bined with an application-specific development. Similarly to human inventions in the area of theoretical computer science, the evolved invention was analyzed: its generality was proven and area and time complexities were determined.
... Unfortunately, standard methods for logic synthesis are not able to solve this problem. In order to find simple multifunctional circuits at the gate level, an evolutionary approach has been utilized in the recent papers [9], [1]. The evolved circuits have up to 5 inputs and outputs and consist of a few tens of gates. ...
... The use of polymorphic gates as building blocks offers an opportunity to design multifunctional digital modules at the gate level.Table II surveys multifunctional combinational modules reported in [9], [1] . For example, using the polymorphic NAND/NOR gate and the standard AND gate it is possible to create a circuit which operates as a two-bit multiplier in one environment and as a two-bit adder in the second environment. ...
Multifunctional digital circuits are circuits composed of polymorphic (multifunctional) gates. In addition to its standard logic function (such as NAND), a polymorphic gate exhibits another logic function (such as NOR) which is activated under a specific condition, for example, when Vdd, temperature or illumination reaches a certain level. This paper describes the evolutionary design of multifunctional combinational circuits at the gate level using a circuit simulator and in a field programmable gate array (FPGA). The FPGA-based implementation exhibits a significant speedup against a highly optimized software simulator.
... Sorting and median networks, adders and parity circuits were successfully designed. Moreover, polymorphic increasing/decreasing sorting networks and odd/even parity circuits were evolved [3]. ...
The first part of this paper introduces a new classification of developmental systems used in the evolutionary design: (1) the infinite development and (2) the finite development. Two sample applicaions are presented demonstrating the ability of this approach to discover novel solutions in the area of the design of digital circuits. In the second part, a formal model of a general developmental system is proposed and the impact of environment on the complexity of the developing objects is investigated.
