Related papers: Counting Ones Without Broadword Operations
We consider the reachability problem on transition systems corresponding to succinct one-counter machines, that is, machines where the counter is incremented or decremented by a value given in binary.
Let $n$ denote the number of elements currently in a data structure. An in-place heap is stored in the first $n$ locations of an array, uses $O(1)$ extra space, and supports the operations: minimum, insert, and extract-min. We introduce an…
This paper depicts an algorithm for solving the Decision Boolean Satisfiability Problem using the binary numerical properties of a Special Decision Satisfiability Problem, parallel execution, object oriented, and short termination. The two…
We consider the quantum complexities of the following three problems: searching an ordered list, sorting an un-ordered list, and deciding whether the numbers in a list are all distinct. Letting N be the number of elements in the input list,…
We investigate the minimum cases for realtime probabilistic machines that can define uncountably many languages with bounded error. We show that logarithmic space is enough for realtime PTMs on unary languages. On binary case, we follow the…
Relaxing the sequential specification of a shared object is a way to obtain an implementation with better performance compared to implementing the original specification. We apply this approach to the Counter object, under the assumption…
New lower bounds on the minimum average Hamming distance of binary codes are derived. The bounds are obtained using linear programming approach.
The discrepancy of a binary string is the maximum (absolute) difference between the number of ones and the number of zeroes over all possible substrings of the given binary string. In this note we determine the minimal discrepancy that a…
Binary embedding is a nonlinear dimension reduction methodology where high dimensional data are embedded into the Hamming cube while preserving the structure of the original space. Specifically, for an arbitrary $N$ distinct points in…
A unary constraint (on the Boolean domain) is a function from {0,1} to the set of real numbers. A free use of auxiliary unary constraints given besides input instances has proven to be useful in establishing a complete classification of the…
We consider the problem of inserting a new item into an ordered list of N-1 items. The length of an algorithm is measured by the number of comparisons it makes between the new item and items already on the list. Classically, determining the…
An $n$-length binary word is $q$-decreasing, $q\geq 1$, if every of its length maximal factor of the form $0^a1^b$ satisfies $a=0$ or $q\cdot a > b$.We show constructively that these words are in bijection with binary words having no…
In standard number-in-hand multi-party communication complexity, performance is measured as the total number of bits transmitted globally in the network. In this paper, we study a variation called local communication complexity in which…
Many streaming algorithms provide only a high-probability relative approximation. These two relaxations, of allowing approximation and randomization, seem necessary -- for many streaming problems, both relaxations must be employed…
Let u be a cyclic word in a free group F_n of finite rank n that has the minimum length over all cyclic words in its automorphic orbit, and let N(u) be the cardinality of the set {v: |v|=|u| and v= \phi(u) for some \phi \in \text {Aut}F_n}.…
Counting the number of ones in a binary stream is a common operation in database, information-retrieval, cryptographic and machine-learning applications. Most processors have dedicated instructions to count the number of ones in a word…
The bin packing problem is to find the minimum number of bins of size one to pack a list of items with sizes $a_1,..., a_n$ in $(0,1]$. Using uniform sampling, which selects a random element from the input list each time, we develop a…
Let $S$ be a complete star-omega semiring and $\Sigma$ be an alphabet. For a weighted $\omega$-restricted one-counter automaton $\mathcal{C}$ with set of states $\{1, \dots, n\}$, $n \geq 1$, we show that there exists a mixed algebraic…
Black-box complexity studies lower bounds for the efficiency of general-purpose black-box optimization algorithms such as evolutionary algorithms and other search heuristics. Different models exist, each one being designed to analyze a…
The paper presents a lower bound for the number of negative eigenvalues of an integral operator with continuous kernel K lying below a nonpositive number t. The estimate is given in terms of some integrals of K.