630 research outputs found
Interval-based Synthesis
We introduce the synthesis problem for Halpern and Shoham's modal logic of
intervals extended with an equivalence relation over time points, abbreviated
HSeq. In analogy to the case of monadic second-order logic of one successor,
the considered synthesis problem receives as input an HSeq formula phi and a
finite set Sigma of propositional variables and temporal requests, and it
establishes whether or not, for all possible evaluations of elements in Sigma
in every interval structure, there exists an evaluation of the remaining
propositional variables and temporal requests such that the resulting structure
is a model for phi. We focus our attention on decidability of the synthesis
problem for some meaningful fragments of HSeq, whose modalities are drawn from
the set A (meets), Abar (met by), B (begins), Bbar (begun by), interpreted over
finite linear orders and natural numbers. We prove that the fragment ABBbareq
is decidable (non-primitive recursive hard), while the fragment AAbarBBbar
turns out to be undecidable. In addition, we show that even the synthesis
problem for ABBbar becomes undecidable if we replace finite linear orders by
natural numbers.Comment: In Proceedings GandALF 2014, arXiv:1408.556
A decidable weakening of Compass Logic based on cone-shaped cardinal directions
We introduce a modal logic, called Cone Logic, whose formulas describe
properties of points in the plane and spatial relationships between them.
Points are labelled by proposition letters and spatial relations are induced by
the four cone-shaped cardinal directions. Cone Logic can be seen as a weakening
of Venema's Compass Logic. We prove that, unlike Compass Logic and other
projection-based spatial logics, its satisfiability problem is decidable
(precisely, PSPACE-complete). We also show that it is expressive enough to
capture meaningful interval temporal logics - in particular, the interval
temporal logic of Allen's relations "Begins", "During", and "Later", and their
transposes
Unitary Noise and the Mermin-GHZ Game
Communication complexity is an area of classical computer science which
studies how much communication is necessary to solve various distributed
computational problems. Quantum information processing can be used to reduce
the amount of communication required to carry out some distributed problems. We
speak of pseudo-telepathy when it is able to completely eliminate the need for
communication. Since it is generally very hard to perfectly implement a quantum
winning strategy for a pseudo-telepathy game, quantum players are almost
certain to make errors even though they use a winning strategy. After
introducing a model for pseudo-telepathy games, we investigate the impact of
erroneously performed unitary transformations on the quantum winning strategy
for the Mermin-GHZ game. The question of how strong the unitary noise can be so
that quantum players would still be better than classical ones is also dealt
with
Complexity of Timeline-Based Planning over Dense Temporal Domains: Exploring the Middle Ground
In this paper, we address complexity issues for timeline-based planning over
dense temporal domains. The planning problem is modeled by means of a set of
independent, but interacting, components, each one represented by a number of
state variables, whose behavior over time (timelines) is governed by a set of
temporal constraints (synchronization rules). While the temporal domain is
usually assumed to be discrete, here we consider the dense case. Dense
timeline-based planning has been recently shown to be undecidable in the
general case; decidability (NP-completeness) can be recovered by restricting to
purely existential synchronization rules (trigger-less rules). In this paper,
we investigate the unexplored area of intermediate cases in between these two
extremes. We first show that decidability and non-primitive recursive-hardness
can be proved by admitting synchronization rules with a trigger, but forcing
them to suitably check constraints only in the future with respect to the
trigger (future simple rules). More "tractable" results can be obtained by
additionally constraining the form of intervals in future simple rules:
EXPSPACE-completeness is guaranteed by avoiding singular intervals,
PSPACE-completeness by admitting only intervals of the forms [0,a] and
[b,[.Comment: In Proceedings GandALF 2018, arXiv:1809.0241
On the Expressiveness of Markovian Process Calculi with Durational and Durationless Actions
Several Markovian process calculi have been proposed in the literature, which
differ from each other for various aspects. With regard to the action
representation, we distinguish between integrated-time Markovian process
calculi, in which every action has an exponentially distributed duration
associated with it, and orthogonal-time Markovian process calculi, in which
action execution is separated from time passing. Similar to deterministically
timed process calculi, we show that these two options are not irreconcilable by
exhibiting three mappings from an integrated-time Markovian process calculus to
an orthogonal-time Markovian process calculus that preserve the behavioral
equivalence of process terms under different interpretations of action
execution: eagerness, laziness, and maximal progress. The mappings are limited
to classes of process terms of the integrated-time Markovian process calculus
with restrictions on parallel composition and do not involve the full
capability of the orthogonal-time Markovian process calculus of expressing
nondeterministic choices, thus elucidating the only two important differences
between the two calculi: their synchronization disciplines and their ways of
solving choices
Branching within Time: an Expressively Complete and Elementarily Decidable Temporal Logic for Time Granularity
Suitable extensions of monadic second-order theories of k
successors have been proposed in the literature to specify in a
concise way reactive systems whose behaviour can be naturally
modeled with respect to a (possibly infinite) set of
differently-grained temporal domains. This is the case, for
instance, of the wide-ranging class of real-time reactive systems
whose components have dynamic behaviours regulated by very
different time constants, e.g., days, hours, and seconds. In this
paper, we focus on the theory of k-refinable downward
unbounded layered structures
MSO[<_{tot},(\downarrow_i)_{i=0}^{k-1}], that is, the theory of infinitely refinable structures consisting of a coarsest domain and an infinite number of finer and finer domains, whose satisfiability problem is nonelementarily decidable. We define a propositional temporal logic counterpart of
MSO[<_{tot},(\downarrow_i)_{i=0}^{k-1}], with set quantification restricted to infinite paths, called CTSL, which features an original mix of linear and branching temporal operators. We prove the expressive completeness of CTSL with respect to such a path fragment of
MSO[<_{tot}, (\downarrow_i)_{i=0}^{k-1}], and show that its satisfiability problem is 2EXPTIME-complete
On Modal {\mu}-Calculus over Finite Graphs with Bounded Strongly Connected Components
For every positive integer k we consider the class SCCk of all finite graphs
whose strongly connected components have size at most k. We show that for every
k, the Modal mu-Calculus fixpoint hierarchy on SCCk collapses to the level
Delta2, but not to Comp(Sigma1,Pi1) (compositions of formulas of level Sigma1
and Pi1). This contrasts with the class of all graphs, where
Delta2=Comp(Sigma1,Pi1)
Model-Checking an Alternating-time Temporal Logic with Knowledge, Imperfect Information, Perfect Recall and Communicating Coalitions
We present a variant of ATL with distributed knowledge operators based on a
synchronous and perfect recall semantics. The coalition modalities in this
logic are based on partial observation of the full history, and incorporate a
form of cooperation between members of the coalition in which agents issue
their actions based on the distributed knowledge, for that coalition, of the
system history. We show that model-checking is decidable for this logic. The
technique utilizes two variants of games with imperfect information and
partially observable objectives, as well as a subset construction for
identifying states whose histories are indistinguishable to the considered
coalition
How do we remember the past in randomised strategies?
Graph games of infinite length are a natural model for open reactive
processes: one player represents the controller, trying to ensure a given
specification, and the other represents a hostile environment. The evolution of
the system depends on the decisions of both players, supplemented by chance.
In this work, we focus on the notion of randomised strategy. More
specifically, we show that three natural definitions may lead to very different
results: in the most general cases, an almost-surely winning situation may
become almost-surely losing if the player is only allowed to use a weaker
notion of strategy. In more reasonable settings, translations exist, but they
require infinite memory, even in simple cases. Finally, some traditional
problems becomes undecidable for the strongest type of strategies
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