We make the following progress on the dot–depth problem: (1) We introduce classes CB n and CL n of starfree languages defined via forbidden patterns in finite automata. It is shown for all n 0 that CB n (CL n) contains level n + 1=2 of the dot–depth hierarchy (Straubing–Thérien hierarchy, resp.). Since we prove that CB n and CL n have decidable membership problems, this yields a lower bound alg...

Large-N multi-matrix loop equations are formulated as quadratic difference equations in concatenation of gluon correlations. Though non-linear, they involve highest rank correlations linearly. They are underdetermined in many cases. Additional linear equations for gluon correlations, associated to symmetries of action and measure are found. Loop equations aren’t differential equations as they i...

This paper addresses the notion of chunk concatenation being associated with sleep-related enhancement consolidation of motor sequence memory, thereby essentially contributing to improvements in sequence execution speed. To this end, element movement times of a multi-joint arm movement sequence incorporated in a recent study by Malangré et al. (2014) were reanalyzed. As sequence elements differ...

Fault-tolerant quantum circuit design can be done by using a set of transversal gates. However, as there is no error correction code with universal gates, several approaches have been proposed which, in combination make fault-tolerant computation possible. Magic state distillation, gauge fixing, switching, concatenation and pieceable fault tolerance are well-known examples such approaches. the ...

In this paper, we consider the list decoding property of codes under insertion and deletion errors (insdel for short). Firstly, analyse decodability random insdel codes. Our result provides a more complete picture on when both happen. Secondly, construct family along with their efficient encoding algorithms through concatenation method which Zyablov-type bound metric