This paper presents one method of using time-bounded Kolmogorov complexity as a measure of the complexity of sets, and outlines a number of applications of this approach to di erent questions in complexity theory. Connections will be drawn among the following topics: NE predicates, ranking functions, pseudorandom generators, and hierarchy theorems in circuit complexity.

This paper presents one method of using time-bounded Kol-mogorov complexity as a measure of the complexity of sets, and outlines a number of applications of this approach to diierent questions in complexity theory. Connections will be drawn among the following topics: NE predicates, ranking functions, pseudorandom generators, and hierarchy theorems in circuit complexity.

Digital circuit design is streamlined process used to improve the performance of a circuit for a particular application. Fast speed, minimum power dissipation and less area are the desirable characteristics of a digital circuit, in general. To meet a particular standard of speed, a compromise in power dissipation and speed is required. Timing elements such as Flip-flop are used as clock generat...

– In this paper the attention is focused on the chaotic dynamics of a new circuit driven by two sinusoidal signals. In particular, it is illustrated that the application of signals with slightly different frequencies enables the novel phenomenon of chaotic beats to be generated. Moreover, the paper shows that the proposed circuit can be considered the simplest nonautonomous circuit able to gene...

The Minimum Circuit Size Problem (MCSP) asks for the size of the smallest boolean circuit that computes a given truth table. It is a prominent problem in NP that is believed to be hard, but for which no proof of NP-hardness has been found. A significant number of works have demonstrated the central role of this problem and its variations in diverse areas such as cryptography, derandomization, p...

We continue the study of the complexity classes VP(Zm) and ΛP(Zm) which was initiated in [AGM15]. We distinguish between “strict” and “lax” versions of these classes and prove some new equalities and inclusions between these arithmetic circuit classes and various subclasses of ACC.

1. Goal: high resolution and large bandwidth ADCs. 2. ADCs: oversampling, noise shaping, (one-bit quantizer); trade speed for resolution; trade analog-circuit accuracy for digital-circuit complexity. 3. Architecture: cascaded 2-0 delta-sigma (2-0 MASH) ADC; p robust stability and speed; high sensitivity to analog-circuit imperfections. 4. Issues of the MASH ADCs: designing the structure; handli...

We show that uniform families of ACC circuits of subexponential size cannot compute the permanent function. This also implies similar lower bounds for certain sets in PP. This is one of the very few examples of a lower bound in circuit complexity where the uniformity condition is essential; it is still unknown if there is any set in Ntime (2 n O(1) ) that does not have nonuniform ACC circuits.

Circuit topologies are introduced which should prove of use to the circuit designer of analog audio amplifiers. The objective is to produce circuits of' modest complexity that overcome the nonlinearities inherent in single-transistor and long-tail pair circuits. This allows amplifiers with excellent linearity to be designed without resorting to overall negative feedback with high loop gains. To...