Abstract: One embodiment accesses a binary decision diagram (BDD) representing a function having n variables, where n?2, wherein: the BDD comprises n layers corresponding to the n variables, respectively; and the BDD has a first variable order where each variable i is at layer i for 1?i?n; and reorders the n variables of the BDD according to a second variable order denoted as ?(i), where each variable i is at layer ?(i) for 1?i?n, by iteratively and alternatingly swapping one or more first disjoint pairs of consecutive layers during each odd iteration and swapping one or more second disjoint pairs of consecutive layers during each even iteration, until the second variable order is achieved, wherein during each iteration, two consecutive layers are swapped only if a current order of two variables at the two consecutive layers differs from an order of the two variables specified by the second variable order.

Abstract: One embodiment accesses a binary decision diagram (BDD) representing a function having n variables, where n?2, wherein the BDD comprises n layers corresponding to the n variables, respectively; and reorders the n variables of the BDD by iteratively and alternating reordering k consecutive layers, where 1<k?n, until a size of the BDD has reached a desired threshold, wherein each iteration comprises: selects k consecutive layers from the n layers, wherein the k consecutive layers selected during a current iteration differ from the k consecutive layers selected during a previous iteration immediately preceding the current iteration; determines a locally optimum variable order of the k consecutive layers; and reorders the k consecutive layers according to the locally optimum variable order of the k consecutive layers.

Abstract: According to certain embodiments, a search query for a search of samples of sensor data is received. The search query indicates one or more requested values of one or more data parameters. The samples are represented by a characteristic function indicating whether a given binary representation represents a sample. A query function representing the one or more requested values is formulated. The query function and the characteristic function are used to identify one or more samples that have the one or more requested values.

Abstract: According to certain embodiments, one or more sets of model samples of model sensor data are accessed. Each set comprises one or more model samples corresponding to an annotation of one or more annotations. The following are performed for each set to yield one or more annotated model characteristic functions: represent each model sample of the each set as a model minterm to yield a set of model minterms; generate a model characteristic function from the set of model minterms, the model characteristic function indicating whether a given minterm is a member of the set of model minterms; and annotate the model characteristic function to yield an annotated model characteristic function. A general model characteristic function is generated from the one or more annotated model characteristic functions.

Abstract: According to certain embodiments, a set of samples of sensor data is accessed. The set of samples records measurements taken by one or more sensors. Each sample is represented as a minterm to yield a set of minterms. A characteristic function is generated from the set of minterms. The characteristic function indicates whether a given minterm is a member of the set of minterms.

Abstract: According to certain embodiments, a set of samples of sensor data is accessed. The set of samples records environmental measurements taken by one or more environmental sensors. A characteristic function is generated from the set of samples. The characteristic function indicates whether a given sample is a member of the set of samples. One or more samples of the set of samples that are associated with a given environmental annotation are identified according to the characteristic function.

Abstract: According to certain embodiments, a characteristic function representing data is received. A first hash code calculated from the characteristic function is received. The characteristic function is transformed to an arithmetic function. A second hash code is calculated from the arithmetic function. If the first hash code equals the second hash code, the data is designated as valid; otherwise, the data is designated as invalid.

Abstract: According to certain embodiments, a first characteristic function representing a first set of samples and a second characteristic function representing a second set of samples are generated. The first characteristic function and the second characteristic function are transformed to a first arithmetic function and a second arithmetic function, respectively. A first hash code and a second hash code are calculated from the first arithmetic function and the second arithmetic function, respectively. If the first hash code equals the second hash code, the first set of samples and the second set of samples are designated as equivalent; otherwise, the first set of samples and the second set of samples are designated as not equivalent.

Abstract: According to certain embodiments, a first Boolean function and a second Boolean function are received. The first Boolean function represents a first data set, and the second Boolean function represents a second data set. The first Boolean function and the second Boolean function are transformed to a first arithmetic function and a second arithmetic function, respectively. A first hash code and a second hash code are calculated from the first arithmetic function and the second arithmetic function, respectively. If the first hash code equals the second hash code, the first Boolean function and the second Boolean function are designated as equivalent; otherwise, the first Boolean function and the second Boolean function are designated as not equivalent.

Abstract: According to certain embodiments, a set of samples of sensor data is accessed. The set of samples records medical measurements taken by one or more medical sensors. A characteristic function is generated from the set of samples. The characteristic function indicates whether a given sample is a member of the set of samples. One or more samples of the set of samples that are associated with a given medical annotation are identified according to the characteristic function.

Abstract: In one embodiment, a method includes receiving first input from a first quick-point controller in a keypad that comprises a plurality of keys; receiving second input from a second quick-point controller in the keypad; and rendering a multi-touch gesture on a display associated with the keypad based on the first and second input.

Abstract: According to one embodiment of the present invention, a method for identifying the occurrence of an event from sensor data streams may be provided. The method may include accessing a plurality of sensor data streams generated by a plurality of sensor sets. Each sensor set may comprise one or more sensors. A sensor data stream may be associated with a user. The user may be co-located with a sensor set that generates the sensor data stream. A relationship between two or more sensor data streams of the plurality of sensor data streams may be identified. The method may further include determining, according to the relationship, that the plurality of sensor data streams corresponds to an event. A notification of an occurrence of the event may be sent.

Abstract: In one embodiment, identifying clusters of words includes accessing a record that records affinities. An affinity between a first and second word describes a quantitative relationship between the first and second word. Clusters of words are identified according to the affinities. A cluster comprises words that are sufficiently affine with each other. A first word is sufficiently affine with a second word if the affinity between the first and second word satisfies one or more affinity criteria. A clustering analysis is performed using the clusters.

Abstract: In one embodiment, a search space of a corpus is searched to yield results. The corpus comprises documents associated with keywords, where each document is associated with at least one keyword indicating at least one theme of the document. One or more keywords are determined to be irrelevant keywords. The search space is refined according to the irrelevant keywords.

Abstract: In one embodiment, a method includes accessing a model of a set of nodes including a session node and multiple linked nodes linked to the session node. The linked nodes include parent nodes and child nodes. A parent node links one or more child nodes to the session node, and a child node has one or more parent nodes linking the child node to the session node. The method includes generating a probability distribution for the set of nodes that distributes probabilities to all linked nodes within a predetermined number of links from the session node. Each child node receives from each of its parent nodes a predetermined fraction of a probability distributed to the parent node, and the parent node uniformly distributes to each of its child nodes the predetermined fraction of the probability distributed to the parent node.

Abstract: In one embodiment, a method includes determining an initial projected size of a BDD representing data for storage. The projected size corresponds to an initial projected number of decision nodes composing the BDD. The method includes determining an initial node structure for the decision nodes of the BDD according to the initial projected size of the BDD. The initial node structure includes for each decision node a variable identifier (ID), a 1-edge pointer, and a 0-edge pointer each represented by a minimum number of bits accommodating the initial projected number of decision nodes composing the BDD.

Abstract: A method for evaluating an erroneous state associated with a target circuit is provided that includes receiving information associated with a target circuit, the information identifying a property within the target circuit to be verified. One or more partitioned ordered binary decision diagram (POBDD) operations are executed using the information in order to identify an erroneous state associated with a sub-space within the target circuit. A path associated with the erroneous state is identified. The path reflects a correlation between an initial state associated with the erroneous state and a point where the erroneous state was encountered.

Abstract: In one embodiment, generating an ontology includes accessing an inverted index comprising a plurality of inverted index lists. An inverted index list may correspond to a term of a language. Each inverted index list may comprise a term identifier of the term and one or more document identifiers indicating one or more documents of a document set in which the term appears. The embodiment also includes generating a term identifier index according to the inverted index. The term identifier index comprises a plurality of sections and each section corresponds to a document. Each section may comprise one or more term identifiers of one or more terms that appear in the document.

Abstract: A system and method for representing digital circuits and systems in multiple partitions of Boolean space, and for performing digital circuit or system validation using the multiple partitions. Decision diagrams are built for the digital circuit or system and pseudo-variables are introduced at decomposition points to reduce diagram size. Pseudo-variables remaining after decomposition are composed and partitioned to represent the digital circuit or system as multiple partitions of Boolean space. Each partition is built in a scheduled order, and is manipulable separately from other partitions.

Abstract: Construct a plurality of first binary decision diagrams (BDDs), each representing a different one of a plurality of words. Construct a plurality of second BDDs, each representing a different one of a plurality of search queries, each of the search queries comprising one or more of the words. Construct a plurality of third BDDs, each representing a different one of a plurality of web pages. Construct a plurality of fourth BDDs, each representing a different one of a plurality of search results, each search result comprising one or more web pages. Construct a plurality of fifth BDDs each representing a different one of a plurality of search tuples, each of the search tuples comprising a different one of the search queries and a different one of the search results. Construct a sixth BDD representing the search queries and the search results.