We generalize the Knuth–Bendix order (KBO) to higher-order terms without λ-abstraction. The restriction of this new order to first-order terms coincides with the traditional KBO. The order has many useful properties, including transitivity, the subterm property, compatibility with contexts (monotonicity), stability under substitution, and well-foundedness. Transfinite weights and argument coeff...

We study the formalization of lambda calculus based on De Bruijn terms. The most interesting aspect is a system of substitution primitives and an accompanying equational theory providing for algebraic proofs. The equational theory can be presented as a confluent and terminating rewriting system providing for proof automation. We prove that parallel reduction is strongly substitutive, the key pr...

Unlike the (classical) Kolakoski sequence on the alphabet {1, 2}, its analogue on {1, 3} can be related to a primitive substitution rule. Using this connection, we prove that the corresponding bi-infinite fixed point is a regular generic model set and thus has a pure point diffraction spectrum. The Kolakoski-(3, 1) sequence is then obtained as a deformation, without losing the pure point diffra...

Oxybiotin, the oxygen analog of biotin (4, 7), possesses biotin-like activity for various micro organisms, the rat, and the chick (4, 8, 15, 17). In this respect, oxybiotin is unique among the vita mins of the B complex, since biological activity is retained in spite of the substitution of the sulfur of the ring by oxygen. It has been demonstrated that the activity of oxybiotin is an intrinsic ...

We define the notion of circular words, then consider on such words a constraint derived from the Fibonacci condition. We give several results on the structure of these circular words, then mention possible applications to various situations: periodic expansion of numbers in numeration systems, “gcd-property” of integer sequences, partition of the prefix of the fixed point of the Fibonacci subs...

Substitution boxes (S-boxes) are of major importance in cryptography as they are used to provide the property of confusion to the corresponding cryptosystem. Thus, a great amount of research is devoted to their study. In this contribution, a new methodology for designing strong S-boxes is studied and two Evolutionary Computation methods, the Particle Swarm Optimization and the Differential Evol...

We generalize the recursive path order (RPO) to higher-order terms without λ-abstraction. This new order fully coincides with the standard RPO on first-order terms also in the presence of currying, distinguishing it from previous work. It has many useful properties, including well-foundedness, transitivity, stability under substitution, and the subterm property. It appears promising as the basi...

in this paper, a faster method for embedding cryptographic information in the image ispresented by expressing the concept of latent prints (steganography). data is encrypted bytwo methods before embedding to increase reliability. then they are embedded into the imageby a button, a method has been expressed to reduce potential noise impact on the wayinformation is encoded.

This paper analyses both the attributes of carsharing transport modes (station-based and free-floating) their relationship with other modes. Users' stakeholders’ perspectives are synthesized from in-depth interviews in Spain. The elicitation comparative advantages two respect to public private vehicles helps identifying factors such as availability parking, road pricing convenience that drive c...