Showing papers on "Equivalence class published in 1991"

Equivalence class analysis of genetic algorithms

Abstract: The conventional understanding of genetic algorithms depends upon analysis by schemata and the notion of intrinsic parallelism. For this reason, only -ary string representations have had any formal basis and non-standard representations and operators have been regarded largely as heuristics, rather than principled algorithms. This paper extends the analysis to general representations through identification of schemata as equivalence classes induced by implicit equivalence relations over the space of chromosomes.

DIATEST: a fast diagnostic test pattern generator for combinational circuits

Abstract: The authors present an efficient algorithm for the generation of diagnostic test patterns which distinguish between two arbitrary single stuck-at faults. The algorithm is able to extend a given set of test patterns which is generated from the viewpoint of fault detection to a diagnostic test pattern set with a diagnostic resolution down to a fault equivalence class. The difficult problem of identifying the equivalence of two faults, analogous to the problem of redundancy identification in ATPG, has been solved. The efficiency of the algorithm is demonstrated by experimental results for a set of benchmark circuits. DIATEST, the implementation of the algorithm, either generates diagnostic test patterns for all distinguishable pairs of faults or identifies pairs of faults as being equivalent for each of the benchmark circuits. >

Protocol analysis of the correspondence of verbal behavior and equivalence class formation

Abstract: In two equivalence experiments, a "think aloud" procedure modeled after Ericsson and Simon's (1980) protocol analysis was implemented to examine subjects' covert verbal responses during matching to sample. The purpose was to identify variables that might explain individual differences in equivalence class formation. The results from Experiment 1 suggested that subjects who formed equivalence classes described the relations among stimuli, whereas those not showing equivalence described sample and comparison stimuli as unitary compounds. Because Experiment 1 only demonstrated a correlation between describing stimulus compounds and the absence of equivalence classes, a second study was conducted. In Experiment 2, equivalence class formation was brought under experimental control through pretraining manipulations that facilitated responding either to stimulus compounds or to relations among stimuli. The results demonstrated that a history of describing stimulus compounds, when compared with describing the relations among the stimuli, interfered with the emergence of stimulus equivalence. These findings clarify individual differences in stimulus equivalence. They also demonstrate the utility of analyzing verbal reports to identify possible variables that can be manipulated experimentally.

The role of instructions in the transfer of ordinal functions through equivalence classes.

Abstract: In two experiments, adult subjects completed match-to-sample training and testing to establish four equivalence classes of four figures each. Then the subjects were taught one three-position sequence consisting of one stimulus from Class 1, one from Class 2, and one from Class 3. Inclusion of Class 4 stimuli in sequences was never reinforced, but two different stimuli from Class 4 appeared as distractors on each sequence trial. Tests assessed whether subjects would produce novel three-position sequences composed of members of Classes 1 through 3 that had not been used in sequence training. Three subjects in Experiment 1 received instructions about the match-to-sample and sequencing tasks, in addition to training contingencies. All 3 demonstrated equivalence class formation after match-to-sample training. After they were taught one sequence with one member of Classes 1 through 3, none of these subjects produced untrained sequences with other equivalence class members reliably. One additional sequence was trained directly; thereafter 1 subject showed some evidence of transfer of the trained ordinal functions across the remaining members of the equivalence classes, but the other 2 did not. Following a review of equivalence class training and testing and a review of the original sequence training, all 3 subjects produced most of the predicted, untrained sequences on tests. Experiment 2 replicated Experiment 1 with 2 adults but omitted all instructions except the minimal ones necessary to initiate responding. Unlike the subjects in Experiment 1, both of these subjects demonstrated virtually complete transfer of ordinal functions through the equivalence classes after direct training on just one sequence composed of one member of Classes 1 through 3.

Stimulus generalization and equivalence classes: a model for natural categories.

Abstract: Two three-member classes were formed by training AB and BC using a conditional discrimination procedure. The A and B stimuli were nonsense syllables, and the C stimuli were sets of "short" or "long" lines. To test for equivalence, C1 or C2 was presented as a sample with A1 and A2 as comparisons. Once the class-related comparison was chosen consistently, different line lengths were substituted for the training lines in the CA tests. In general, the likelihood of choosing a given comparison was an inverse function of the difference in the length of the test line from the training line. Stimuli in an equivalence class became functionally related not only to each other but also to novel stimuli that resembled a member of the equivalence class. The combination of primary generalization and equivalence class formation, then, can serve as a model to account for the development of naturally occurring categories.

Learning classification rules from database in the context of knowledge acquisition and representation

Abstract: A method for learning knowledge from a database is used to address the bottleneck of manual knowledge acquisition. An attempt is made to improve representation with the assistance of experts and from computer resident knowledge. The knowledge representation is described in the framework of a conceptual schema consisting of a semantic model and an event model. A concept classifies a domain into different subdomains. As a method of knowledge acquisition, inductive learning techniques are used for rule generation. The theory of rough sets is used in designing the learning algorithm. Examples of certain concepts are used to induce general specifications of the concepts called classification rules. The basic approach is to partition the information into equivalence classes and to derive conclusions based on equivalence relations. In a sense, what is involved is a data-reduction process, where the goal is to reduce a large database of information to a small number of rules describing the domain. This completely integrated approach includes user interface, semantics, constraints, representations of temporal events, induction, etc. >

Implicit manipulation of equivalence classes using binary decision diagrams

Abstract: A novel representation called an equivalence class characterization function is defined. It can implicitly represent all equivalence classes with a compact characteristic function that will have at most n outputs. Using binary decision diagrams (BDDs) and the concept of the equivalence class characterization function, very large problem instances can be represented. For manipulating equivalence classes efficiently, a Boolean operator called a compatible projection operator is proposed. Conceptually, the compatible projection operator is used to uniquely select a single element from each equivalence class to characterize the class. In manipulating equivalence classes, the compatible projection operator is used to implicitly derive an encoding function from the equivalence relation that encodes the equivalence class information symbolically. An efficient implementation is described based on BDDs that is applied to very large problem instances. >

State space generation for degradable multiprocessor systems

Abstract: Degradable multiprocessors can have a large number of different structural configurations (states) after being altered by faults. Many such states may be equivalent relative to their overall effect on a system's ability to perform. Hence, depending on the performability measure, the number of states can often be reduced to a much smaller set of representative configurations, one for each equivalence class. An algorithm that generates these representatives and determines the size of each equivalence class is presented. The algorithm assumes that performance is invariant under structural symmetries and thus employs a symmetry permutation group. The information so obtained permits construction of a stochastic process model that supports the performability measure in question. The group-theoretic concepts on which the algorithm is based are presented, and its complexity is considered. The use of the algorithm to construct a performability model is illustrated, and possible extensions are addressed. >

Concurrent Error Detection in Sequential Circuits Using Convolutional Codes

Abstract: Concurrent error detection schemes in digital systems are often based upon error-detecting codes. In [9], we presented a methodology for encoding the states of sequential machines using convolutional codes for on-line detection of sequencing errors. In conjunction with this methodology, we defined an equivalence relation on convolutional codes that exhaustively characterizes the possible transient error detection capabilities and complexities of sequential machine realizations based upon convolutional codes. In this paper, we determine the number of equivalence classes of (n, k, 1) convolutional codes generated by minimal encoders requiring k memory elements and provide a procedure for generating representatives from each equivalence class.

Perceptual limits, perceptual equivalence classes, and a robot's sensori-computational capabilities (extended abstract)

Abstract: Considers a theory of planning, sensing and action in which the fundamental building blocks are, in effect, the 'recognizable sets'-that is, the places in the world that the robot can recognize and distinguish between. To this end the authors observe that viewing the world through sensors, partitions the world into 'perceptual equivalence classes.' The more information the sensors provide, the 'finer' this partition is. Various possible partitions of the world fit into a lattice structure. This lattice structure captures the information or knowledge state about the world. Using this theory the authors develop notions of task-directed planning and show how history can be used to direct actions and gain information. The authors investigate the structure of the recognizability lattice and its relationship to the world. The authors consider how to compute perceptual equivalence classes both from a model, and incrementally, from the world. Finally, the authors investigate mathematical properties that can help the robot generate disambiguating strategies to gain information about the world to accomplish a task. >

Utilizing logic information in multi-level timing simulation

Abstract: Multi-level simulation arith a dynamic model level selection mechanism is a technique for increasing simulation efficiency. Implementation considerations dictate a pessimistic dynamic model selection mechanjsm which could rault in longer execution times than a normal simulation of a flattened logic network. Om equivalence class concept lessens the impact of the pessimistic xlection mechanism by detecting currently dormant logic blocka with reaped to an input transition. Earlier work on timing simulation incorporated multiple model levels with a dynamic model level selection mechanism[l]. Similar multiple model level approaches have revealed comparable execution increases of three to five times over that of simulation using the lowest model levels[lO]. Unfortunately, due to practical limitations, the dynamic model selection mechanism is more pessimistic than necessary and results in an appreciable performance degradation due to the unnecessary invocation of lower model levels. In this work, we describe a technique to lessen the impact of the pessimistic dynamic model selection mechanism. Our technique called equivalence classes is based on anticipating a subcircuit block’s output activityin response to a transition at the block’s input node. We fmt start with the description of our simulation environment and then describe OUT equivalence classes concept. We continue with presentation of algorithms to extract equivalence classes from gate level logic descriptions, present implementation details and results, and finally our conclusions.

Partitioning and reorganization of hierarchical circuits for DFT

Abstract: To make VLSI circuits more testable, design-for-testability (DFT) and built-in self-test (BIST) techniques are often employed. These techniques typically assume a register/gate level decomposition of the overall circuit. In general, the given user hierarchy is not appropriate for embedding various testable design methodologies (TDMs). This paper describes a new canonical partitioning of a circuit into disjoint subcircuits, referred to as clouds and registers. A salient feature of this partitioning is the attempt to preserve the user hierarchy as much as possible. This enables easy identification of equivalence among various clouds of the circuit. The authors also show how this canonical partitioning can be used for three specific TDMs, namely full scan, partial scan and BILBO designs. For the case of full scan, deterministic tests are generated for one cloud in each equivalence class, and replicated for all clouds in that class. These tests are organized to form a test set for the entire circuit. Test vectors are edited to correspond to the order of flip-flops in the scan paths of the circuit. Analytical expressions for the reduction in the number of test vectors due to this canonical partitioning are derived and substantiated with experimental results. >

Equivalence Classes and Generalized Coherent States in Quantum Measurement.

Abstract: The notion of an equivalence class, which was first considered by Jauch, is introduced into generalized coherent-state formalism in quantum measurement. Two equivalent states in Jauch’s treatment cannot be distinguished by measurement of any observables of a physical system (the definition of an observable also being ambiguous). In our approach it is possible in principle, but becomes more difficult asN→∞,N being the number of molecules constructing a detector; we cannot distinguish them at all in the large-N limit. Two models are presented, which show that the notion of equivalence class is well suited to the generalized coherentstate approach. It is also shown that in each model a statistical operator and its mixed-state part belong to the same equivalence class.

ldempotents in Nest Algebras

Abstract: The algebraic equivalence and similarity classes of idempotents within a nest algebra Alg/l are completely characterized. We obtain necessary and sufficient conditions for two idempotents to he equivalent or similar. Our criterion yields examples illustrating pathology and also shows that to each equivalence class of idempotents there corresponds a “dimension function” from pxb into Nv {IX }. We complete the characterization of the algebraic equivalence classes by proving that any dimension function corresponds to an equivalence class of idempotents. Also, to each sequence of dimension functions, there corresponds a commuting sequence of idempotents. A criterion is obtained for when an idempotent is similar to a subidempotent of another. The mapping which sends an equivalence class (or idempotent) to its associated dimension function plays a role in the nest algebra theory analogous to the role played by the mapping sending a projection in a Type I W*-algebra to its center valued trace. WC prove that almost commuting, similar idempotents are homotopic; this contrasts with the situation in certain C*-algebras. Using this, we show that similar, stmultaneously diagonalizable idempotents are homotopic, and in the continuous nest case, every diagonal idempotent is homotopic to a core projection.

Scalable, parallel performance environments

Abstract: It is shown that new techniques are needed to analyze and present performance data from massively parallel systems. Although parallel programs contain many tasks, typically, there are only a few equivalence classes of task behavior. The author is planning to incorporate algorithms for performance data clustering and display (i.e. equivalence class identification) performance data presentation. >