Characterizations of flowchartable recursions
نویسندگان
چکیده
منابع مشابه
Fractals, recursions, divisibility
The self similar (fractal) structure of the Pascal triangle of binomial coefficients modulo some fixed prime has been known for some time and explored in detail. It turns out that such a fractal structure is the common property arithmetical functions of two variables possessing a more general recursive relation (R) f(i,j) = af(i-l,j) + bf(i 1,j-1) where a and b are fixed integers. 'When a, b ar...
متن کاملThe ABC of Hyper Recursions
Each family of Gauss hypergeometric functions fn = 2F1(a + ε1n, b + ε2n; c + ε3n; z), for fixed εj = 0,±1 (not all εj equal to zero) satisfies a second order linear difference equation of the form Anfn−1 + Bnfn + Cnfn+1 = 0. Because of symmetry relations and functional relations for the Gauss functions, many of the 26 cases (for different εj values) can be transformed into each other. We give a...
متن کاملPseudorandom recursions II
We present our earlier results (not included in Hars and Petruska due to space and time limitations), as well as some updated versions of those, and a few more recent pseudorandom number generator designs. These tell a systems designer which computer word lengths are suitable for certain high-quality pseudorandom number generators, and which constructions of a large family of designs provide lo...
متن کاملRunning Modulus Recursions
Fix integers b ≥ 2 and k ≥ 1. Define the sequence {zn} recursively by taking z0 to be any integer, and for n ≥ 1, take zn to be the least nonnegative residue of bzn−1 modulo (n + k). Since the modulus increases by 1 when stepping from one term to the next, such a definition will be called a running modulus recursion or rumor for short. While the terms of such sequences appear to bounce around i...
متن کاملConstructing Recursions by Similarity
A formal specification can describe software models which are difficult to program. Transformational methods based on fold/unfold strategies have been proposed to palliate this problem. The objective of applying transformations is to filter out a new version of the specification where recursion may be introduced by a folding step. Among many problems, the “eureka” about when and how to define a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 1973
ISSN: 0022-0000
DOI: 10.1016/s0022-0000(73)80032-7