Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the gap between ess(f) and cnf_size(f)   Given a Boolean function f, the quantity ess(f) denotes the largest set of
assignments that falsify f, no two of which falsify a common implicate of f.
Although ess(f)$ is clearly a lower bound on cnf_size(f) (the minimum number of
clauses in a CNF formula for f), Cepek et al. showed that it is not, in
general, a tight lower bound. They gave examples of functions f for which there
is a small gap between ess(f) and cnf_size(f). We demonstrate significantly
larger gaps. We show that the gap can be exponential in n for arbitrary Boolean
functions, and Theta(sqrt{n}) for Horn functions, where n is the number of
variables of f. We also introduce a natural extension of the quantity ess(f),
which we call ess_k(f), which is the largest set of assignments, no k of which
falsify a common implicate of f.

28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex