Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Expressive Completeness of Bernays-Sch\"onfinkel-Ramsey
  Separation Logic   This paper investigates the satisfiability problem for Separation Logic, with
unrestricted nesting of separating conjunctions and implications, for prenex
formulae with quantifier prefix in the language $\exists^*\forall^*$, in the
cases where the universe of possible locations is either countably infinite or
finite. In analogy with first-order logic with uninterpreted predicates and
equality, we call this fragment Bernays-Sch\"onfinkel-Ramsey Separation Logic
[BSR(SLk)]. We show that, unlike in first-order logic, the (in)finite
satisfiability problem is undecidable for BSR(SLk) and we define two
non-trivial subsets thereof, that are decidable for finite and infinite
satisfiability, respectively, by controlling the occurrences of universally
quantified variables within the scope of separating implications, as well as
the polarity of the occurrences of the latter. The decidability results are
obtained by a controlled elimination of separating connectives, described as
(i) an effective translation of a prenex form Separation Logic formula into a
combination of a small number of \emph{test formulae}, using only first-order
connectives, followed by (ii) a translation of the latter into an
equisatisfiable first-order formula.

21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga