Related papers: A Gray Code for cross-bifix-free sets
Cross-bifix-free sets are sets of words such that no prefix of any word is a suffix of any other word. In this paper, we introduce a general constructive method for the sets of cross-bifix-free binary words of fixed length. It enables us to…
A cross-bifix-free code is a set of words in which no prefix of any length of any word is the suffix of any word in the set. Cross-bifix-free codes arise in the study of distributed sequences for frame synchronization. We provide a new…
Cross-bifix-free sets are sets of words such that no prefix of any word is a sufix of any other word. In this paper, we introduce a general constructive method for the sets of cross-bifix-free q-ary words of fixed length. It enables us to…
A bidimensional bifix (in short bibifix) of a square matrix T is a square submatrix of T which occurs in the top-left and bottom-right corners of T. This allows us to extend the definition of bifix-free words and cross-bifix-free set of…
A prefix normal word is a binary word with the property that no substring has more $1$s than the prefix of the same length. By proving that the set of prefix normal words is a bubble language, we can exhaustively list all prefix normal…
Based on BRGC inspired order relations we give Gray codes and a generating algorithm for $q$-ary words avoiding a prescribed factor. These generalize an early 2001 result and a very recent one published by some of the present authors, and…
A Gray code is a listing structure for a set of combinatorial objects such that some consistent (usually minimal) change property is maintained throughout adjacent elements in the list. While Gray codes for m-ary strings have been…
We investigate the construction of prefix-free and fix-free codes with specified codeword compositions. We present a polynomial time algorithm which constructs a fix-free code with the same codeword compositions as a given code for a…
We generalize a well-known algorithm for the generation of all subsets of a set in lexicographic order with respect to the sets as lists of elements (subset-lex order). We obtain algorithms for various combinatorial objects such as the…
We provide a trace partitioned Gray code for the set of q-ary strings avoiding a pattern constituted by k consecutive equal symbols. The definition of this Gray code is based on two different constructions, according to the parity of q.…
A variable-length code is a fix-free code if no codeword is a prefix or a suffix of any other codeword. In a fix-free code any finite sequence of codewords can be decoded in both directions, which can improve the robustness to channel noise…
We investigate the structural relationship between prefix-free codes over the binary alphabet and a class of unlabeled rooted trees, which we call \emph{symmetric} trees. We establish a canonical correspondence between prefix-free codes and…
We consider the following combinatorial question. Let $$ S_0 \subset S_1 \subset S_2 \subset ...\subset S_m $$ be nested sets, where #$(S_i) = i$. A move consists of altering one of the sets $S_i$, $1 \le i \le m-1$, in a manner so that the…
Symmetric fix-free codes are prefix condition codes in which each codeword is required to be a palindrome. Their study is motivated by the topic of joint source-channel coding. Although they have been considered by a few communities they…
We study skew-tolerant Gray codes, which are Gray codes in which changes in consecutive codewords occur in adjacent positions. We present the first construction of asymptotically non-vanishing skew-tolerant Gray codes, offering an…
Given a set $F$ of words, one associates to each word $w$ in $F$ an undirected graph, called its extension graph, and which describes the possible extensions of $w$ on the left and on the right. We investigate the family of sets of words…
A combinatorial Gray code for a set of combinatorial objects is a sequence of all combinatorial objects in the set so that each object is derived from the preceding object by changing a small part. In this paper we design a Gray code for…
We introduce a new construction for the balancing of non-binary sequences that make use of Gray codes for prefix coding. Our construction provides full encoding and decoding of sequences, including the prefix. This construction is based on…
In 2011, Fici and Lipt\'ak introduced prefix normal words. A binary word is prefix normal if it has no factor (substring) that contains more occurrences of the letter 1 than the prefix of the same length. Among the open problems regarding…
The optimal prefix-free machine U is a universal decoding algorithm used to define the notion of program-size complexity H(s) for a finite binary string s. Since the set of all halting inputs for U is chosen to form a prefix-free set, the…