Theoretical Computer Science

Given an order of the underlying alphabet, we can lift it to the states of a finite deterministic automaton: to compare states we use the order of the strings reaching them. When the order on strings is the co-lexicographic one and ...

• The best possible encodings (compression) of DFAs and NFAs are obtained by imposing a suitable order on their states.

We prove a complexity dichotomy theorem for a class of Holant problems on 3-regular bipartite graphs. Given an arbitrary nonnegative weighted symmetric constraint function f = [ x 0 , x 1 , x 2 , x 3 ], we prove that the bipartite ...

The price of explainability for a clustering task can be defined as the unavoidable loss, in terms of the objective function, if we force the final partition to be explainable. Here, we study this price for the k-centers and maximum-...

Unified Temporal Logic (UTL) combines all characteristics of traditional Linear Temporal Logic (LTL) and Propositional Projection Temporal Logic (PPTL). It can be used to describe full regular and omega-regular properties, which are ...

As usual λ ( G ) denotes the edge-connectivity of the graph G. It was shown in [2] that every graph G contains a spanning ( λ ( G ) + 1 )-partite subgraph H such that λ ( H ) = λ ( G ) and one can find such a spanning subgraph in ...

We study two scheduling games on parallel-batching machines with activation cost, where each game involves n jobs being processed on m parallel-batching identical machines. Each job, as an agent, selects a machine (more precisely, a ...

Bennett's notion of depth is usually considered to describe, roughly speaking, the usefulness and internal organization of the information encoded into an object such as an infinite binary sequence. We consider a natural way to ...

• We present a robust way to relativize the notion of Bennett's logical depth.
• We ...