Sound-and-Complete Algorithms for Checking the Dynamic Controllability of Conditional Simple Temporal Networks with Uncertainty

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 that are based on the propagation of labeled constraints and demonstrates their practicality

Extending Conditional Simple Temporal Networks with Partially Shrinkable Uncertainty

The proper handling of temporal constraints is crucial in many domains. As a particular challenge, temporal constraints must be also handled when different specific situations happen (conditional constraints) and when some event occurrences can be only observed at run time (contingent constraints). In this paper we introduce Conditional Simple Temporal Networks with Partially Shrinkable Uncertainty (CSTNPSUs), in which contingent constraints are made more flexible (guarded constraints) and they are also specified as conditional constraints. It turns out that guarded constraints require the ability to reason on both kinds of constraints in a seamless way. In particular, we discuss CSTNPSU features through a motivating example and, then, we introduce the concept of controllability for such networks and the related sound checking algorithm

Foundations of Dispatchability for Simple Temporal Networks with Uncertainty

Simple Temporal Networks (STNs) are a widely used formalism for representing and reasoning about tem- poral constraints on activities. The dispatchability of an STN was originally defined as a guarantee that a specific real-time execution algorithm would necessarily satisfy all of the STN’s constraints while preserv- ing maximum flexibility but requiring minimal computation. A Simple Temporal Network with Uncertainty (STNU) augments an STN to accommodate actions with uncertain durations. However, the dispatchability of an STNU was defined differently: in terms of the dispatchability of its so-called STN projections. It was then argued informally that this definition provided a similar real-time execution guarantee, but without specifying the execution algorithm. This paper formally defines a real-time execution algorithm for STNUs that similarly preserves maximum flexibility while requiring minimal computation. It then proves that an STNU is dispatch- able if and only if every run of that real-time execution algorithm necessarily satisfies the STNU’s constraints no matter how the uncertain durations play out. By formally connecting STNU dispatchability to an explicit real-time execution algorithm, the paper fills in important elements of the foundations of the dispatchability of STNUs

A Better Algorithm for Converting an STNU into Minimal Dispatchable Form

A Simple Temporal Network with Uncertainty (STNU) is a data structure for representing and reasoning about temporal constraints on activities, including those with uncertain durations. An STNU is dispatchable if it can be flexibly and efficiently executed in real time while guaranteeing that all relevant constraints are satisfied. Typically, dispatchability requires inserting conditional wait constraints, thereby forming an Extended STNU (ESTNU). The number of edges in an ESTNU affects the computational work that must be done during real-time execution. The MinDispESTNU problem is that of finding an equivalent dispatchable ESTNU having a minimal number of edges. Recent work presented an O(k n3)-time algorithm for solving the MinDispESTNU problem, where n is the number of timepoints and k is the number of actions with uncertain durations. A subsequent paper presented a faster O(n3)-time algorithm, but it has been shown to be incomplete. This paper presents a new O(mn+ n2 k+ n2 log n)-time algorithm for solving the MinDispESTNU problem, where m is the number of constraints in the network. The correctness of the algorithm is based on a novel theory of the canonical form of nested diamond structures. An empirical evaluation demonstrates the order-of-magnitude improvement in performance

Flexible temporal constraint management in modularized processes

Managing temporal process constraints in modularized processes is an important task, both during the design, as it allows the reuse of temporal (child) process models, and during the checking of temporal properties of processes, as it avoids the necessity of ‘‘unfolding’’ child processes within the main process model. Taking into account the capability of providing modular solutions, modeling and checking temporal features of processes is still an open problem in the context of process-aware information systems. In this paper, we present and discuss a novel approach to represent flexible temporal constraints in modularized time-aware BPMN process models. To support temporal flexibility, allowed task durations are represented through guarded ranges that allow a limited (guarded) restriction of task durations during process execution if it is necessary to guarantee the satisfaction of all temporal constraints. We, then, propose how to derive a compact representation of the overall temporal behavior of such time-aware BPMN models. Such compact representation of child processes allows us to check the dynamic controllability (DC) of a parent timeaware process model without ‘‘unfolding’’ the child process models. Dynamic controllability guarantees that process models can have process instances (i.e., executions) satisfying all the temporal constraints for any possible combination of allowed durations of tasks and child processes. Possible approaches for even more flexibility by solving some kinds of DC violations are then introduced. We use a real process model from a healthcare domain as a motivating example, and we also present a proof-of-concept prototype confirming the concrete applicability of the solutions we propose, followed by an experimental evaluation

Canonical Form of Nested Diamond Structures

A Simple Temporal Network with Uncertainty (STNU) is a data structure for representing and reasoning about time in contexts where some actions may have uncertain, but bounded durations. An STNU is dynamically controllable (DC) if there exists a strategy for executing its controllable timepoints such that no matter how the uncertain durations turn out, within their known bounds, all relevant constraints in the network will necessarily be satisfied. Several polynomial-time DC-checking algorithms have been presented in the literature. A real-time execution strategy, called RTE^*, has been defined that preserves maximum flexibility while requiring minimal real-time computation; however, that strategy only guarantees a successful execution if: (1) the network is extended to accommodate conditional wait constraints; and (2) the network satisfies an additional property called dispatchability, that is stronger than dynamic controllability. This report presents a novel theory of the dispatchability of Extended STNUs (ESTNUs) that is based on the canonical form of nested diamond structures. Each such structure entails an ordinary constraint that must be satisfied by any dispatchable ESTNU. This theory provides an avenue through which to explore more efficient algorithms for finding equivalent dispatchable networks having a minimal number of edges, which is important for limiting the computational requirements during real-time execution

Speeding Up the RUL¯ Dynamic-Controllability-Checking Algorithm for Simple Temporal Networks with Uncertainty

A Simple Temporal Network with Uncertainty (STNU) in- cludes real-valued variables, called time-points; binary differ- ence constraints on those time-points; and contingent links that represent actions with uncertain durations. STNUs have been used for robot control, web-service composition, and business processes. The most important property of an STNU is called dynamic controllability (DC); and algorithms for checking this property are called DC-checking algorithms. The DC- checking algorithm for STNUs with the best worst-case time- complexity is the RUL− algorithm due to Cairo, Hunsberger and Rizzi. Its complexity is O(mn + k2n + kn log n), where n is the number of time-points, m is the number of constraints, and k is the number of contingent links. It is expected that this worst-case complexity cannot be improved upon. However, this paper provides a new algorithm, called RUL2021, that improves its performance in practice by an order of magnitude, as demonstrated by a thorough empirical evaluation

Robust Execution of Probabilistic STNs

A Probabilistic Simple Temporal Network (PSTN) is a formalism for representing and reasoning about actions subject to temporal constraints, where some action durations may be uncontrollable, modeled using continuous probability density functions. Recent work aims to manage this kind of uncertainty during execution by approximating a PSTN by a Simple Temporal Network with Uncertainty (STNU) (for which well-known execution strategies exist) and using an STNU execution strategy to execute the PSTN, hoping that its probabilistic action durations will not cause any constraint violations. This paper presents significant improvements to the robust execution of PSTNs. Our approach is based on a recent, faster algorithm for finding negative cycles in non-DC STNUs. We also formally prove that many of the constraints included in others' work are unnecessary and that our algorithm can take advantage of a flexible real-time execution algorithm to react to observations of contingent durations that may fall outside the fixed STNU bounds. The paper presents an empirical evaluation of our approach that provides evidence of its effectiveness in robustly executing PSTNs derived from a publicly available benchmark

Faster Dynamic-Consistency Checking for Conditional Simple Temporal Networks

A Conditional Simple Temporal Network (CSTN) is a structure for representing and reasoning about time in domains where temporal constraints may be conditioned on outcomes of observations made in real time. A CSTN is dynamically consistent (DC) if there is a strategy for executing its time-points such that all relevant constraints will necessarily be satisfied no matter which outcomes happen to be observed. The literature on CSTNs contains only one sound-and-complete DC-checking algorithm that has been implemented and empirically evaluated. It is a graph-based algorithm that propagates labeled constraints/edges. A second algorithm has been proposed, but not evaluated. It aims to speed up DC checking by more efficiently dealing with so-called negative q-loops. This paper presents a new two-phase approach to DC-checking for CSTNs. The first phase focuses on identifying negative q-loops and labeling key time-points within them. The second phase focuses on computing (labeled) distances from each time-point to a single sink node. The new algorithm, which is also sound and complete for DC-checking, is then empirically evaluated against both pre-existing algorithms and shown to be much faster across not only previously published benchmark problems, but also a new set of benchmark problems. The results show that, on DC instances, the new algorithm tends to be an order of magnitude faster than both existing algorithms. On all other benchmark cases, the new algorithm performs better than or equivalently to the existing algorithms

Propagating Piecewise-Linear Weights in Temporal Networks

This paper presents a novel technique using piecewise-linear functions (PLFs) as weights on edges in the graphs of two kinds of temporal networks to solve several previously open problems. Generalizing constraint-propagation rules to accom- modate PLF weights requires implementing a small handful of functions. Most problems are solved by inserting one or more edges with an initial weight of \u3b4 (a variable), then using the modified rules to propagate the PLF weights. For one kind of network, a new set of propagation rules is introduced to avoid a non-termination issue that arises when propagating PLF weights. The paper also presents two new results for determining the tightest horizon that can be imposed while preserving a network\u2019s dynamic consistency/controllability