This paper is concerned with the synthesis of invariants in programs with arrays. More specifically, we consider properties concerning array contents up to a permutation. For instance, to prove a sorting procedure, one has to show that the result is sorted, but also that it is a permutation of the initial array. In order to analyze this kind of properties, we define an abstract interpretation w...

An equidistant permutation array A(r, I ; u ) is a t' x r array defined on a symbol set V such that each row of the array is a permutation of the symbol set V and any two distinct rows of A have precisely A common column entries. Given r and i.. one can ask for the largest u such that an A(r, 2.; v) exists or find the smallest v such that an A(r, I; u ) exists which cannot be extended to an A(r...

This paper considers the symbolic determinant computation. The aptness of permutation method for symbolic determinant is justified and a new efficient algorithm is proposed to implement the permutation method. Exploiting the fact computers perform arithmetic operations fast, the proposed algorithm generate all the permutations without manipulation on additional 2nd array or redundancies found i...

Permutation codes and multi-permutation have been widely considered due to their various applications, especially in flash memory. In this paper, we consider permutation against a burst of stable deletions. particular, propose construction correcting deletion length s , with redundancy log xmln...

We design an algorithm that generates multiset permutations in O(1) time from permutation to permutations, using only data structures of arrays. The previous O(1) time algorithm used pointers, causing O(n) time to access an element in a permutation, where n is the size of permutations. The central idea in our algorithm is tree traversal. We associate permutations with the leaves of a tree. By t...

We investigate retransmission permutation arrays (RPAs) that are motivated by applications in overlapping channel transmissions. An RPA is an n × n array in which each row is a permutation of {1, . . . , n}, and for 1 6 i 6 n, all n symbols occur in each i × ⌈

In-situ permutation algorithms are algorithms to permute an array of n items without using a second array. Few space is needed when one proceeds permuting along a cycle. Thus, those algorithms first search for one element called leader on each cycle of the permutation. Then they move the items cycle by cycle. A great fraction of the runtime is spent with testing whether elements are leaders. We...

A significant improvement in memory fault tolerance, beyond what is already provided by the use of an appropriate error-correcting code (ECC), can be achieved by electronic chip swapping, without any compromise of data integrity as large numbers of faults are allowed to accumulate. Since most large and medium-sized semiconductor memories are organized so that each bit position of the system wor...

The RC4 stream cipher has been designed by Ron Rivest for RSA Data Security in 1987, and was a propriety algorithm until 1994. Currently, RC4 is extremely popular in commercial domain and widely used in network protocols such as Secure Sockets Layer (SSL), Transport Layer Security (TLS), Wired Equivalent Privacy (WEP), Wi-Fi Protected Access (WPA) etc. RC4 uses an S-Box S = (S[0], . . . , S[N −...