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

Dealing with Changes of Time-Aware Processes

The proper handling of temporal process constraints is crucial in many application domains. Contemporary process-aware information systems (PAIS), however, lack a sophisticated support of time-aware processes. As a particular challenge, the execution of time-aware processes needs to be flexible as time can neither be slowed down nor stopped. Hence, it should be possible to dynamically adapt time-aware process instances to cope with unforeseen events. In turn, when applying such dynamic changes, it must be re-ensured that the resulting process instances are temporally consistent; i.e., they still can be completed without violating any of their temporal constraints. This paper presents the ATAPIS framework which extends well established process change operations with temporal constraints. In particular, it provides pre- and post-conditions for these operations that guarantee for the temporal consistency of the changed process instances. Furthermore, we analyze the effects a change has on the temporal properties of a process instance. In this context, we provide a means to significantly reduce the complexity when applying multiple change operations. Respective optimizations will be crucial to properly support the temporal perspective in adaptive PAIS

Reducing Dynamic-Consistency (DC) Checking for Conditional Simple Temporal Networks (CSTNs) with Bounded Reaction Times to Standard DC Checking for CSTNs

Recent work on Conditional Simple Temporal Networks (CSTNs) has introduced the problem of checking the dynamic consistency (DC) property for the case where the reaction of an execution strategy to observations is bounded below by some fixed \u3b5 > 0. This paper shows how the \u3b5-DC-checking problem can be easily reduced to the standard DC-checking problem for CSTNs. Given any CSTN S with k observation time-points, the paper defines a new CSTN S0 that is the same as S, except that it includes k new observation time-points. For each observation time-point P? in S that observes some proposition p, the time-point P? in S0 is demoted from an observation time-point to an ordinary time-point; and the job of observing p is taken over by a new observation time-point P0? that is constrained to occur exactly \u3b5 after P?. The paper proves that S is \u3b5-DC if and only if S0 is DC; and shows that the application of the \u3b5-DC- checking constraint-propagation rules to S is equivalent to the application of the corresponding DC-checking constraint-propagation rules to S0. Two versions of these results are presented, depending on whether a dynamic strategy for S0 can react instantaneously or only after some arbitrarily small, positive delay. Finally, the paper demonstrates empirically that the performance of building S0 and DC-checking it is even better than \u3b5-DC-checking the original instance S

Dynamic-Consistency Checking for Conditional Simple Temporal Networks: Strengthening the Theoretical Foundations and Presenting a Faster Algorithm

Recent work on Conditional Simple Temporal Networks (CSTNs) has focused on checking the dynamic consistency (DC) property for the case where an execution strategy can react instantaneously to observations. Three alternative semantics for such strategies\u2014IR-dynamic, 0-dynamic, and \u3c0-dynamic\u2014have been presented. However, the most practical DC-checking algorithm has only been analyzed with respect to the IR semantics. Meanwhile, 0-dynamic strategies were shown to permit a kind of circular dependence among simultaneous observations, making them impossible to implement, whereas \u3c0-dynamic strategies prohibit this kind of circularity. Whether IR-dynamic strategies allow this kind of circularity and, if so, what the consequences would be for the above-mentioned DC-checking algorithm remained open questions. This paper makes the following contributions: (1) it shows that IR-dynamic strategies do allow circular dependence and, thus, that the IR semantics does not properly capture instantaneous reactivity; (2) it shows that one of the constraint-propagation rules from the IR-DC-checking algorithm is unsound with respect to the IR semantics; (3) it presents a simpler DC-checking algorithm, called the \u3c0-DC-checking algorithm, that uses half of the rules from the earlier algorithm, and that it proves is sound and complete with respect to the \u3c0-DC semantics; (4) it empirically evaluates the new algorithm. Thus, the paper places practical DC checking for CSTNs in the case of instantaneous reaction on a solid theoretical foundation

Analyzing the Impact of Process Change Operations on Time-Aware Processes

The proper handling of temporal constraints is crucial in many application domains. Contemporary process-aware information systems, however, still lack a sophisticated support of time-aware processes. As a particular challenge, by nature, (most) time-aware processes need to be quite flexible as time can neither be slowed down nor stopped. Hence it must be possible to dynamically adapt a time-aware process instance in order to cope with unforeseen events. In turn, when applying dynamic changes to a time-aware process it crucial that the resulting process instance is again sound as well as temporally consistent; i.e., it must still be possible to complete the process instance without violating any of its temporal constraints. This paper extends existing process change operations, which ensure soundness of the resulting process instance, by additionally considering temporal constraints. Furthermore, it provides pre- and post-conditions that ensure that the resulting process instance is again temporally consistent. Finally, we analyze the impact a change has on the overall temporal properties of a process instance and---based on the results---provide means to significantly reduce the complexity of the required time calculations. The latter is crucial to ensure scalability of the approach. The approach has been prototypically implemented in the AristaFlow BPM Suite

Dynamic Controllability Checking for Conditional Simple Temporal Networks with Uncertainty: New Sound-and-Complete Algorithms based on Constraint Propagation

A Conditional Simple Temporal Network with Uncertainty (CSTNU) is a data structure for representing and reasoning about time. CSTNUs incorporate "observation time-points" from Conditional Simple Temporal Networks (CSTNs) and "contingent links" from Simple Temporal Networks with Uncertainty (STNUs). A CSTNU is "dynamically controllable" (DC) if there exists a strategy for executing its time-points that guarantees the satisfaction of all relevant constraints no matter how the uncertainty associated with its observation time-points and contingent links is resolved in real time. This paper presents the first sound-and-complete DC-checking algorithms for CSTNUs based on the propagation of labeled constraints and demonstrates their practicality

Conditional Simple Temporal Networks with Uncertainty and Decisions

A Conditional Simple Temporal Network with Uncertainty (CSTNU) is a formalism able to model temporal plans subject to both conditional constraints and uncertain durations. The combination of these two characteristics represents the uncontrollable part of the network. That is, before the network starts executing, we do not know completely which time points and constraints will be taken into consideration nor how long the uncertain durations will last. Dynamic Controllability (DC) implies the existence of a strategy scheduling the time points of the network in real time depending on how the uncontrollable part behaves. Despite all this, CSTNUs fail to model temporal plans in which a few conditional constraints are under control and may therefore influence (or be influenced by) the uncontrollable part. To bridge this gap, this paper proposes Conditional Simple Temporal Networks with Uncertainty and Decisions (CSTNUDs) which introduce decision time points into the specification in order to operate on this conditional part under control. We model the dynamic controllability checking (DC-checking) of a CSTNUD as a two-player game in which each player makes his moves in his turn at a specific time instant. We give an encoding into timed game automata for a sound and complete DC-checking. We also synthesize memoryless execution strategies for CSTNUDs proved to be DC and carry out an experimental evaluation with Esse, a tool that we have designed for CSTNUDs to make the approach fully automated

Reasoning and querying bounds on differences with layered preferences

Artificial intelligence largely relies on bounds on differences (BoDs) to model binary constraints regarding different dimensions, such as time, space, costs, and calories. Recently, some approaches have extended the BoDs framework in a fuzzy, \u201cnoncrisp\u201d direction, considering probabilities or preferences. While previous approaches have mainly aimed at providing an optimal solution to the set of constraints, we propose an innovative class of approaches in which constraint propagation algorithms aim at identifying the \u201cspace of solutions\u201d (i.e., the minimal network) with their preferences, and query answering mechanisms are provided to explore the space of solutions as required, for example, in decision support tasks. Aiming at generality, we propose a class of approaches parametrized over user\u2010defined scales of qualitative preferences (e.g., Low, Medium, High, and Very High), utilizing the resume and extension operations to combine preferences, and considering different formalisms to associate preferences with BoDs. We consider both \u201cgeneral\u201d preferences and a form of layered preferences that we call \u201cpyramid\u201d preferences. The properties of the class of approaches are also analyzed. In particular, we show that, when the resume and extension operations are defined such that they constitute a closed semiring, a more efficient constraint propagation algorithm can be used. Finally, we provide a preliminary implementation of the constraint propagation algorithms

Process time patterns: A formal foundation

Companies increasingly adopt process-aware information systems (PAISs) to model, execute, monitor, and evolve their business processes. Though the handling of temporal constraints (e.g., deadlines or time lags between activities) is crucial for the proper support of business processes, existing PAISs vary significantly regarding the support of the temporal perspective. Both the formal specification and the operational support of temporal constraints constitute fundamental challenges in this context. In previous work, we introduced process time patterns, which facilitate the comparison and evaluation of PAISs in respect to their support of the temporal perspective. Furthermore, we provided empirical evidence for these time patterns. To avoid ambiguities and to ease the use as well as the implementation of the time patterns, this paper formally defines their semantics. To additionally foster the use of the patterns for a wide range of process modeling languages and to enable pattern integration with existing PAISs, the proposed semantics are expressed independently of a particular process meta model. Altogether, the presented pattern formalization will be fundamental for introducing the temporal perspective in PAISs