On the complexity of minimum inference of regular sets

We prove results concerning the computational tractability of some problems related to determining minimum realizations of finite samples of regular sets by finite automata and regular expressions

Induction of Topological Environment Maps from Sequences of Visited Places

In this paper we address the problem of topologically mapping environments which contain inherent perceptual aliasing caused by repeated environment structures. We propose an approach that does not use motion or odometric information but only a sequence of deterministic measurements observed by traversing an environment. Our algorithm implements a stochastic local search to build a small map which is consistent with local adjacency information extracted from a sequence of observations. Moreover, local adjacency information is incorporated to disambiguate places which are physically different but appear identical to the robots senses. Experiments show that the proposed method is capable of mapping environments with a high degree of perceptual aliasing, and that it infers a small map quickly

On the exact learnability of graph parameters: The case of partition functions

We study the exact learnability of real valued graph parameters $f$ which are known to be representable as partition functions which count the number of weighted homomorphisms into a graph $H$ with vertex weights $\alpha$ and edge weights $\beta$. M. Freedman, L. Lov\'asz and A. Schrijver have given a characterization of these graph parameters in terms of the $k$-connection matrices $C(f,k)$ of $f$. Our model of learnability is based on D. Angluin's model of exact learning using membership and equivalence queries. Given such a graph parameter $f$, the learner can ask for the values of $f$ for graphs of their choice, and they can formulate hypotheses in terms of the connection matrices $C(f,k)$ of $f$. The teacher can accept the hypothesis as correct, or provide a counterexample consisting of a graph. Our main result shows that in this scenario, a very large class of partition functions, the rigid partition functions, can be learned in time polynomial in the size of $H$ and the size of the largest counterexample in the Blum-Shub-Smale model of computation over the reals with unit cost.Comment: 14 pages, full version of the MFCS 2016 conference pape

The Complexity of Fixed-Height Patterned Tile Self-Assembly

We characterize the complexity of the PATS problem for patterns of fixed height and color count in variants of the model where seed glues are either chosen or fixed and identical (so-called non-uniform and uniform variants). We prove that both variants are NP-complete for patterns of height 2 or more and admit O(n)-time algorithms for patterns of height 1. We also prove that if the height and number of colors in the pattern is fixed, the non-uniform variant admits a O(n)-time algorithm while the uniform variant remains NP-complete. The NP-completeness results use a new reduction from a constrained version of a problem on finite state transducers.Comment: An abstract version appears in the proceedings of CIAA 201

Modelling Data Mining Dynamic Code Attributes with Scheme Definition Technique

Data mining is a technique used in differentdisciplines to search for significant relationships among variablesin large data sets. One of the important steps on data mining isdata preparation. On these step, we need to transform complexdata with more than one attributes into representative format fordata mining algorithm. In this study, we concentrated on thedesigning a proposed system to fetch attributes from a complexdata such as product ID. Then the proposed system willdetermine the basic price of each product based on hiddenrelationships among the attributes of data. These researchesconclude that the proposed system accuracy of precision rate is98.7% and recall rate are 70.27%

Modelling Data Mining Dynamic Code Attributes With Scheme Definition Technique

Data mining is a technique used in differentdisciplines to search for significant relationships among variablesin large data sets. One of the important steps on data mining isdata preparation. On these step, we need to transform complexdata with more than one attributes into representative format fordata mining algorithm. In this study, we concentrated on thedesigning a proposed system to fetch attributes from a complexdata such as product ID. Then the proposed system willdetermine the basic price of each product based on hiddenrelationships among the attributes of data. These researchesconclude that the proposed system accuracy of precision rate is98.7% and recall rate are 70.27%

Information-theoretic bound on the energy cost of stochastic simulation

Physical systems are often simulated using a stochastic computation where different final states result from identical initial states. Here, we derive the minimum energy cost of simulating a complex data set of a general physical system with a stochastic computation. We show that the cost is proportional to the difference between two information-theoretic measures of complexity of the data - the statistical complexity and the predictive information. We derive the difference as the amount of information erased during the computation. Finally, we illustrate the physics of information by implementing the stochastic computation as a Gedankenexperiment of a Szilard-type engine. The results create a new link between thermodynamics, information theory, and complexity.Comment: 5 pages, 1 figur