This invited Descriptional Complexity of Formal Systems lecture provides an opportunity to raise awareness of the tight connection that exists between Kolmogorov Complexity and Circuit Complexity, and to argue that this connection is useful and interesting. Kolmogorov complexity has been used to provide examples of complete sets for classes such as EXP and PSPACE that are fundamentally differen...

Circuit expressions were introduced to provide a natural link between Computational Learning and certain aspects of Structural Complexity. Upper and lower bounds on the learnability of circuit expressions are known. We study here the case in which the circuit expressions are of low (time-bounded) Kolmogorov complexity. We show that these are polynomial-time learnable from membership queries in ...

We present a randomized method for computing the min-plus product (a.k.a. tropical product) of two $n \times n$ matrices, yielding faster algorithm solving all-pairs shortest path problem (APSP) in dense $n$-node directed graphs with arbitrary edge weights. In real random-access machine model, where additions and comparisons reals are unit cost (but all other operations have logarithmic cost), ...

We introduce wire length as a salient complexity measure for analyzing the circuit complexity of sensory processing in biological neural systems. This new complexity measure is applied in this paper to two basic computational problems that arise in translationand scale-invariant pattern recognition, and hence appear to be useful as benchmark problems for sensory processing. We present new circu...

A quantum circuit must be preprocessed before implementing on NISQ devices due to the connectivity constraint. Quantum mapping (QCM) transforms into an equivalent one that is compliant with device’s architecture constraint by adding SWAP gates. The QCM problem asks minimal number of auxiliary gates, and NP-complete. complexity fixed parameters studied in paper. We give exact algorithm for QCM, ...

Circuits composed of threshold gates (McCulloch-Pitts neurons, or perceptrons) are simplified models of neural circuits with the advantage that they are theoretically more tractable than their biological counterparts. However, when such threshold circuits are designed to perform a specific computational task, they usually differ in one important respect from computations in the brain: they requ...

This paper presents a hybrid algorithm on P/G networks of Mesh+Tree topology for ASICs. Based on existing algorithms, equivalent circuit method and TLM-ADI method, our algorithm is of linear complexity to solve P/G networks of Mesh+Tree topology. First, it uses equivalent circuit approach to compress the Mesh+Tree P/G circuit into the circuit only of Mesh topology, which is a linear complexity ...