6 research outputs found
From local to global consistency in temporal constraint networks
AbstractWe study the problem of global consistency for several classes of quantitative temporal constraints which include inequalities, inequations and disjunctions of inequations. In all cases that we consider we identify the level of local consistency that is necessary and sufficient for achieving global consistency and present an algorithm which achieves this level. As a byproduct of our analysis, we also develop an interesting minimal network algorithm
Keynote: The first-order logic of signals
Formalizing properties of systems with continuous dynamics is a challenging task. In this paper, we propose a formal framework for specifying and monitoring rich temporal properties of real-valued signals. We introduce signal first-order logic (SFO) as a specification language that combines first-order logic with linear-real arithmetic and unary function symbols interpreted as piecewise-linear signals. We first show that while the satisfiability problem for SFO is undecidable, its membership and monitoring problems are decidable. We develop an offline monitoring procedure for SFO that has polynomial complexity in the size of the input trace and the specification, for a fixed number of quantifiers and function symbols. We show that the algorithm has computation time linear in the size of the input trace for the important fragment of bounded-response specifications interpreted over input traces with finite variability. We can use our results to extend signal temporal logic with first-order quantifiers over time and value parameters, while preserving its efficient monitoring. We finally demonstrate the practical appeal of our logic through a case study in the micro-electronics domain
Deciding whether the ordering is necessary in a Presburger formula
Automata, Logic and Semantic
Representing and Integrating Multiple Calendars
Whenever humans refer to time, they do so with respect to a
specific underlying calendar. So do most software applications.
However, most theoretical
models of time refer to time with respect to the integers (or reals).
Thus, there is a mismatch between the theory and the application of
temporal reasoning.
To lessen this gap, we propose a formal, theoretical definition of a
calendar and show how one may specify dates, time points, time
intervals, as well as sets of time points, in terms of constraints
with respect to a given calendar. Furthermore, when multiple
applications using different calendars wish to work together, there is
a need to integrate those calendars together into a single, unified
calendar. We show how this can be done.
(Also cross-referenced as UMIACS-TR-97-12
Probabilistic Temporal Databases, I: Algebra
Dyreson and Snodgrass have drawn attention to the fact that in many
temporal database applications, there is often uncertainty present
about the start time of events, the end time of events, the duration of
events, etc. When the granularity of time is small (e.g. milliseconds),
a statement such as "Packet p was shipped sometime during the
first 5 days of January, 1998" leads to a massive amount of uncertainty
(5 times 24 times 60 times 60 times 1000) possibilities. As noted by
Zaniolo et. al., past
attempts to deal with uncertainty in databases have been restricted
to relatively small amounts of uncertainty in attributes.
Dyreson and Snodgrass have taken an important first
step towards solving this problem.
In this paper, we first introduce the syntax of Temporal-Probabilistic
(TP) relations and then show how they can be converted to an explicit,
significantly more space-consuming form called Annotated Relations.
We then present a {\em Theoretical Annotated Temporal
Algebra} (TATA). Being explicit, TATA
is convenient for specifying how the
algebraic operations should behave, but is impractical to use because
annotated relations are overwhelmingly large.
Next, we present a Temporal Probabilistic Algebra (TPA).
We show that our definition of the TP-Algebra
provides a correct implementation of TATA despite the fact that
it operates on implicit, succinct TP-relations instead of the
overwhelmingly large annotated relations.
Finally, we report on timings for an implementation of the TP-Algebra
built on top of ODBC.
(Also cross-referenced as UMIACS-TR-99-09