We investigate the deterministic rational transductions computable by constant-depth, polysize circuits. To this end, we first propose a framework of independent interest to express functions of variable output length using circuits, and argue for its pertinence. We then provide a general characterization of the set of transductions realizable by such circuits, relying on a notion of continuity...

The representation of functions as low-degree polyno-mials over various rings has provided many insights in the theory of small-depth circuits. We survey some of the closure properties, upper bounds, and lower bounds obtained via this approach.

In this paper we define a new descriptional complexity measure for Deterministic Finite Automata, BC-complexity, as an alternative to the state complexity. We prove that for two DFAs with the same number of states BC-complexity can differ exponentially. In some cases minimization of DFA can lead to an exponential increase in BC-complexity, on the other hand BC-complexity of DFAs with a large st...

We study the following question, communicated to us by Miklós Ajtai: Can all explicit (e.g., polynomial time computable) functions f : ({0, 1}) → {0, 1} be computed by word circuits of constant size? Here, a word circuit is an acyclic circuit where each wire holds a word (i.e., an element of {0, 1}) and each gate G computes some binary operation gG : ({0, 1}) → {0, 1}, defined for all word leng...

Ontology-based data access is an approach to organizing access to a database augmented with a logical theory. In this approach query answering proceeds through a reformulation of a given query into a new one which can be answered without any use of theory. Thus the problem reduces to the standard database setting. However, the size of the query may increase substantially during the reformulatio...

In this note, we consider the minimum number of NOT operators in a Boolean formula representing a Boolean function. In circuit complexity theory, the minimum number of NOT gates in a Boolean circuit computing a Boolean function f is called the inversion complexity of f . In 1958, Markov determined the inversion complexity of every Boolean function and particularly proved that ⌈log 2 (n + 1)⌉ NO...

We construct explicit Boolean square matrices whose rectifier complexity (OR-complexity) differs significantly from the complexity of the complement matrices. This note can be viewed as an addition to the material of [2, §5.6]. Recall that rectifier (m,n)-circuit is an oriented graph with n vertices labeled as inputs and m vertices labeled as outputs. Rectifier circuit (ORcircuit) implements a ...

(i) a theorem that is closely related to Erdös and Rado’s sunflower lemma, and claims a stronger statement in most cases, (ii) a new approach to prove the exponential monotone circuit complexity of the clique problem, (iii) NC 6= NP through the impossibility of a Boolean circuit with poly-log depth to compute cliques, based on the conctruction of (ii), and (iv) P 6= NP through the exponential c...

Specific and sensitive operation of circuit breakers makes an individual position for them in power networks. Circuit breakers are at the central gravity of variations and execution operations. Therefore, an optimum operation is the main reason to investigate about new gases to be used in MV and HV circuit breakers instead of SF6. The arc process has enormous complexity because of hydrodynamic ...