2,499 research outputs found
Reasoning about transfinite sequences
We introduce a family of temporal logics to specify the behavior of systems
with Zeno behaviors. We extend linear-time temporal logic LTL to authorize
models admitting Zeno sequences of actions and quantitative temporal operators
indexed by ordinals replace the standard next-time and until future-time
operators. Our aim is to control such systems by designing controllers that
safely work on -sequences but interact synchronously with the system in
order to restrict their behaviors. We show that the satisfiability problem for
the logics working on -sequences is EXPSPACE-complete when the
integers are represented in binary, and PSPACE-complete with a unary
representation. To do so, we substantially extend standard results about LTL by
introducing a new class of succinct ordinal automata that can encode the
interaction between the different quantitative temporal operators.Comment: 38 page
Modeling and Analyzing Adaptive User-Centric Systems in Real-Time Maude
Pervasive user-centric applications are systems which are meant to sense the
presence, mood, and intentions of users in order to optimize user comfort and
performance. Building such applications requires not only state-of-the art
techniques from artificial intelligence but also sound software engineering
methods for facilitating modular design, runtime adaptation and verification of
critical system requirements.
In this paper we focus on high-level design and analysis, and use the
algebraic rewriting language Real-Time Maude for specifying applications in a
real-time setting. We propose a generic component-based approach for modeling
pervasive user-centric systems and we show how to analyze and prove crucial
properties of the system architecture through model checking and simulation.
For proving time-dependent properties we use Metric Temporal Logic (MTL) and
present analysis algorithms for model checking two subclasses of MTL formulas:
time-bounded response and time-bounded safety MTL formulas. The underlying idea
is to extend the Real-Time Maude model with suitable clocks, to transform the
MTL formulas into LTL formulas over the extended specification, and then to use
the LTL model checker of Maude. It is shown that these analyses are sound and
complete for maximal time sampling. The approach is illustrated by a simple
adaptive advertising scenario in which an adaptive advertisement display can
react to actions of the users in front of the display.Comment: In Proceedings RTRTS 2010, arXiv:1009.398
A Modal Logic for Subject-Oriented Spatial Reasoning
We present a modal logic for representing and reasoning about space seen from the subject\u27s perspective. The language of our logic comprises modal operators for the relations "in front", "behind", "to the left", and "to the right" of the subject, which introduce the intrinsic frame of reference; and operators for "behind an object", "between the subject and an object", "to the left of an object", and "to the right of an object", employing the relative frame of reference. The language allows us to express nominals, hybrid operators, and a restricted form of distance operators which, as we demonstrate by example, makes the logic interesting for potential applications. We prove that the satisfiability problem in the logic is decidable and in particular PSpace-complete
Generalized planning: Non-deterministic abstractions and trajectory constraints
We study the characterization and computation of general policies for families of problems that share a structure characterized by a common reduction into a single abstract problem. Policies mu that solve the abstract problem P have been shown to solve all problems Q that reduce to P provided that mu terminates in Q. In this work, we shed light on why this termination condition is needed and how it can be removed. The key observation is that the abstract problem P captures the common structure among the concrete problems Q that is local (Markovian) but misses common structure that is global. We show how such global structure can be captured by means of trajectory constraints that in many cases can be expressed as LTL formulas, thus reducing generalized planning to LTL synthesis. Moreover, for a broad class of problems that involve integer variables that can be increased or decreased, trajectory constraints can be compiled away, reducing generalized planning to fully observable nondeterministic planning
On Pebble Automata for Data Languages with Decidable Emptiness Problem
In this paper we study a subclass of pebble automata (PA) for data languages
for which the emptiness problem is decidable. Namely, we introduce the
so-called top view weak PA. Roughly speaking, top view weak PA are weak PA
where the equality test is performed only between the data values seen by the
two most recently placed pebbles. The emptiness problem for this model is
decidable. We also show that it is robust: alternating, nondeterministic and
deterministic top view weak PA have the same recognition power. Moreover, this
model is strong enough to accept all data languages expressible in Linear
Temporal Logic with the future-time operators, augmented with one register
freeze quantifier.Comment: An extended abstract of this work has been published in the
proceedings of the 34th International Symposium on Mathematical Foundations
of Computer Science (MFCS) 2009}, Springer, Lecture Notes in Computer Science
5734, pages 712-72
On Relaxing Metric Information in Linear Temporal Logic
Metric LTL formulas rely on the next operator to encode time distances,
whereas qualitative LTL formulas use only the until operator. This paper shows
how to transform any metric LTL formula M into a qualitative formula Q, such
that Q is satisfiable if and only if M is satisfiable over words with
variability bounded with respect to the largest distances used in M (i.e.,
occurrences of next), but the size of Q is independent of such distances.
Besides the theoretical interest, this result can help simplify the
verification of systems with time-granularity heterogeneity, where large
distances are required to express the coarse-grain dynamics in terms of
fine-grain time units.Comment: Minor change
Linear Temporal Logic and Propositional Schemata, Back and Forth (extended version)
This paper relates the well-known Linear Temporal Logic with the logic of
propositional schemata introduced by the authors. We prove that LTL is
equivalent to a class of schemata in the sense that polynomial-time reductions
exist from one logic to the other. Some consequences about complexity are
given. We report about first experiments and the consequences about possible
improvements in existing implementations are analyzed.Comment: Extended version of a paper submitted at TIME 2011: contains proofs,
additional examples & figures, additional comparison between classical
LTL/schemata algorithms up to the provided translations, and an example of
how to do model checking with schemata; 36 pages, 8 figure
Incompleteness of States w.r.t. Traces in Model Checking
Cousot and Cousot introduced and studied a general past/future-time
specification language, called mu*-calculus, featuring a natural time-symmetric
trace-based semantics. The standard state-based semantics of the mu*-calculus
is an abstract interpretation of its trace-based semantics, which turns out to
be incomplete (i.e., trace-incomplete), even for finite systems. As a
consequence, standard state-based model checking of the mu*-calculus is
incomplete w.r.t. trace-based model checking. This paper shows that any
refinement or abstraction of the domain of sets of states induces a
corresponding semantics which is still trace-incomplete for any propositional
fragment of the mu*-calculus. This derives from a number of results, one for
each incomplete logical/temporal connective of the mu*-calculus, that
characterize the structure of models, i.e. transition systems, whose
corresponding state-based semantics of the mu*-calculus is trace-complete
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