5 research outputs found
Subclasses of Presburger Arithmetic and the Weak EXP Hierarchy
It is shown that for any fixed , the -fragment of
Presburger arithmetic, i.e., its restriction to quantifier alternations
beginning with an existential quantifier, is complete for
, the -th level of the weak EXP
hierarchy, an analogue to the polynomial-time hierarchy residing between
and . This result completes the
computational complexity landscape for Presburger arithmetic, a line of
research which dates back to the seminal work by Fischer & Rabin in 1974.
Moreover, we apply some of the techniques developed in the proof of the lower
bound in order to establish bounds on sets of naturals definable in the
-fragment of Presburger arithmetic: given a -formula
, it is shown that the set of non-negative solutions is an ultimately
periodic set whose period is at most doubly-exponential and that this bound is
tight.Comment: 10 pages, 2 figure
Heterogeneous Active Agents
Over the years, many different agent programming languages have been
proposed. In this paper, we propose a concept called Agent Programs
using which, the way an agent should act in various situations can be
declaratively specified by the creator of that agent. Agent Programs
may be built on top of arbitrary pieces of software code and may be used
to specify what an agent is obliged to do, what an agent may do, and
what an agent may not do. In this paper, we define several successively
more sophisticated and epistemically satisfying declarative semantics
for agent programs, and study the computation price to be paid (in terms
of complexity) for such epistemic desiderata. We further show that
agent programs cleanly extend well understood semantics for logic
programs, and thus are clearly linked to existing results on logic
programming and nonmonotonic reasoning. Last, but not least, we have
built a simulation of a Supply Chain application in terms of our theory,
building on top of commercial software systems such as Microsoft Access
and ESRI's Map Object.
(Also cross-referenced as UMIACS-TR-98-15