Abstract: A method, system, and apparatus for authenticating transactions and records is disclosed. An information-based indicium includes an article bearing a first identifier, wherein the first identifier substantially prevents a single user from accumulating multiple articles bearing the same first identifier, and a first digital certificate that is derived in part by encoding the first identifier, wherein the first digital certificate and the article may be presented together to authenticate the indicium by comparing the first digital certificate and the first identifier.

Abstract: A method, system, and apparatus for authenticating transactions and records is disclosed. A nonce stamp is a physical article that is relatively difficult to copy illicitly, and that bears a “nonce” number. The “nonce” is a relatively unique identifier, in that it is chosen from a distribution such that any given user/customer is extremely unlikely to obtain two nonce stamps bearing the same nonce. The method includes: presenting a nonce stamp having a nonce number; presenting a numbered digital certificate derived securely from the nonce number; and authenticating the transaction by comparing the number on the digital certificate and the nonce number. The digital certificate is typically obtained by users/customers in exchange for the purchase price of a desired transaction. The apparatus is an information-based indicium including a nonce stamp, and a digital certificate including a number derived securely from the nonce.

Abstract: A method, system, and apparatus for authenticating transactions and records is disclosed. A nonce stamp is a physical article that is relatively difficult to copy illicitly, and that bears a “nonce” number. The “nonce” is a relatively unique identifier, in that it is chosen from a distribution such that any given user/customer is extremely unlikely to obtain two nonce stamps bearing the same nonce. The method includes: presenting a nonce stamp having a nonce number; presenting a numbered digital certificate derived securely from the nonce number; and authenticating the transaction by comparing the number on the digital certificate and the nonce number. The digital certificate is typically obtained by users/customers in exchange for the purchase price of a desired transaction. The apparatus is an information-based indicium including a nonce stamp, and a digital certificate including a number derived securely from the nonce.

Abstract: The method provides a sound and complete online decision method for the combination of canonizable and solvable theories together with uninterpreted function and predicate symbols. It also provides the representation of a solution state in terms of theory-wise solution sets that are used to capture the equality information extracted from the processed equalities. The method includes a context-sensitive canonizer that uses theory-specific canonizers and the solution state to obtain the canonical form of an expression with respect to the given equality information. Moreover, included is the variable abstraction operation for reducing and equality between term to an equality between variables and an enhanced solution state. The closure operation for propagating equality information between solution sets for individual theories uses the theory-specific solvers. The invention teaches a modular method for combining solvers and canonizers into a combination decision procedure.

Abstract: Method, system, and apparatus for authenticating transactions and records. A nonce stamp is a physical article that is relatively difficult to copy illicitly, and that bears a “nonce” number. The “nonce” is a relatively unique identifier, in that it is chosen from a distribution such that any given user/customer is extremely unlikely to obtain two nonce stamps bearing the same nonce. The method includes: presenting a nonce stamp having a nonce number; presenting a numbered digital certificate derived securely from the nonce number; and authenticating the transaction by comparing the number on the digital certificate and the nonce number. The digital certificate is typically obtained by users/customers in exchange for the purchase price of a desired transaction. The apparatus is an information-based indicium including a nonce stamp, and a digital certificate including a number derived securely from the nonce.

Abstract: An improved transducer array includes a two-dimensional array of multilayer actuators, capable of producing very high displacement with low input voltage, integrally packaged with conditioning electronics. Preferred microcomposite actuators use multiple layers of stacked electrostrictive ceramics and conductive materials. The actuators are aligned in a two-dimensional array and can be integrated with the conditioning electronics in a variety of packaging systems. A preferred packaging system is a flexible high density interconnected multi-chip module which has the integrated circuit chips disposed in a substrate, interconnection layers disposed thereon and the multilayer composite actuators disposed on the surface of the interconnection structure. The actuators in this packaged array may be optionally addressed individually or in blocks, depending on the application intended.