5,159 research outputs found
Hybrid SAT-Based Consistency Checking Algorithms for Simple Temporal Networks with Decisions
A Simple Temporal Network (STN) consists of time points modeling temporal events and constraints modeling the minimal and maximal temporal distance between them. A Simple Temporal Network with Decisions (STND) extends an STN by adding decision time points to model temporal plans with decisions. A decision time point is a special kind of time point that once executed allows for deciding a truth value for an associated Boolean proposition. Furthermore, STNDs label time points and constraints by conjunctions of literals saying for which scenarios (i.e., complete truth value assignments to the propositions) they are relevant. Thus, an STND models a family of STNs each obtained as a projection of the initial STND onto a scenario. An STND is consistent if there exists a consistent scenario (i.e., a scenario such that the corresponding STN projection is consistent). Recently, a hybrid SAT-based consistency checking algorithm (HSCC) was proposed to check the consistency of an STND. Unfortunately, that approach lacks experimental evaluation and does not allow for the synthesis of all consistent scenarios. In this paper, we propose an incremental HSCC algorithm for STNDs that (i) is faster than the previous one and (ii) allows for the synthesis of all consistent scenarios and related early execution schedules (offline temporal planning). Then, we carry out an experimental evaluation with KAPPA, a tool that we developed for STNDs. Finally, we prove that STNDs and disjunctive temporal networks (DTNs) are equivalent
Dynamic Consistency of Conditional Simple Temporal Networks via Mean Payoff Games: a Singly-Exponential Time DC-Checking
Conditional Simple Temporal Network (CSTN) is a constraint-based
graph-formalism for conditional temporal planning. It offers a more flexible
formalism than the equivalent CSTP model of Tsamardinos, Vidal and Pollack,
from which it was derived mainly as a sound formalization. Three notions of
consistency arise for CSTNs and CSTPs: weak, strong, and dynamic. Dynamic
consistency is the most interesting notion, but it is also the most challenging
and it was conjectured to be hard to assess. Tsamardinos, Vidal and Pollack
gave a doubly-exponential time algorithm for deciding whether a CSTN is
dynamically-consistent and to produce, in the positive case, a dynamic
execution strategy of exponential size. In the present work we offer a proof
that deciding whether a CSTN is dynamically-consistent is coNP-hard and provide
the first singly-exponential time algorithm for this problem, also producing a
dynamic execution strategy whenever the input CSTN is dynamically-consistent.
The algorithm is based on a novel connection with Mean Payoff Games, a family
of two-player combinatorial games on graphs well known for having applications
in model-checking and formal verification. The presentation of such connection
is mediated by the Hyper Temporal Network model, a tractable generalization of
Simple Temporal Networks whose consistency checking is equivalent to
determining Mean Payoff Games. In order to analyze the algorithm we introduce a
refined notion of dynamic-consistency, named \epsilon-dynamic-consistency, and
present a sharp lower bounding analysis on the critical value of the reaction
time \hat{\varepsilon} where the CSTN transits from being, to not being,
dynamically-consistent. The proof technique introduced in this analysis of
\hat{\varepsilon} is applicable more in general when dealing with linear
difference constraints which include strict inequalities
Checking Dynamic Consistency of Conditional Hyper Temporal Networks via Mean Payoff Games (Hardness and (pseudo) Singly-Exponential Time Algorithm)
In this work we introduce the \emph{Conditional Hyper Temporal Network
(CHyTN)} model, which is a natural extension and generalization of both the
\CSTN and the \HTN model. Our contribution goes as follows. We show that
deciding whether a given \CSTN or CHyTN is dynamically consistent is
\coNP-hard. Then, we offer a proof that deciding whether a given CHyTN is
dynamically consistent is \PSPACE-hard, provided that the input instances are
allowed to include both multi-head and multi-tail hyperarcs. In light of this,
we continue our study by focusing on CHyTNs that allow only multi-head or only
multi-tail hyperarcs, and we offer the first deterministic (pseudo)
singly-exponential time algorithm for the problem of checking the
dynamic-consistency of such CHyTNs, also producing a dynamic execution strategy
whenever the input CHyTN is dynamically consistent. Since \CSTN{s} are a
special case of CHyTNs, this provides as a byproduct the first
sound-and-complete (pseudo) singly-exponential time algorithm for checking
dynamic-consistency in CSTNs. The proposed algorithm is based on a novel
connection between CSTN{s}/CHyTN{s} and Mean Payoff Games. The presentation of
the connection between \CSTN{s}/CHyTNs and \MPG{s} is mediated by the \HTN
model. In order to analyze the algorithm, we introduce a refined notion of
dynamic-consistency, named -dynamic-consistency, and present a sharp
lower bounding analysis on the critical value of the reaction time
where a \CSTN/CHyTN transits from being, to not being,
dynamically consistent. The proof technique introduced in this analysis of
is applicable more generally when dealing with linear
difference constraints which include strict inequalities.Comment: arXiv admin note: text overlap with arXiv:1505.0082
Complexity Bounds for the Controllability of Temporal Networks with Conditions, Disjunctions, and Uncertainty
In temporal planning, many different temporal network formalisms are used to
model real world situations. Each of these formalisms has different features
which affect how easy it is to determine whether the underlying network of
temporal constraints is consistent. While many of the simpler models have been
well-studied from a computational complexity perspective, the algorithms
developed for advanced models which combine features have very loose complexity
bounds. In this paper, we provide tight completeness bounds for strong, weak,
and dynamic controllability checking of temporal networks that have conditions,
disjunctions, and temporal uncertainty. Our work exposes some of the subtle
differences between these different structures and, remarkably, establishes a
guarantee that all of these problems are computable in PSPACE
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