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

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

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

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

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

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

A note on speeding up DC-checking for STNUs

A Simple Temporal Network with Uncertainty (STNU) includes real-valued variables, called time-points; binary difference constraints on those time-points; and contingent links that represent actions with uncertain durations. 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 $O(mn + k^2n + knlog n)$, where $n$ is the number of time-points, $m$ is the number of constraints (equivalently, the number of edges in the STNU graph), 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 implementation of the algorithm that improves its performance in practice by an order of magnitude, as demonstrated by a thorough empirical evaluation

A Streamlined Model of Conditional Simple Temporal Networks - Semantics and Equivalence Results

A Conditional Simple Temporal Network (CSTN) augments a Simple Temporal Network to include a new kind of time-points, called observation time-points. The execution of an observation time-point generates information in real time, specifically, the truth value of a propositional letter. In addition, time-points and temporal constraints may be labeled by conjunctions of (positive or negative) propositional letters. A CSTN is called dynamically consistent (DC) if there exists a dynamic strategy for executing its time-points such that no matter how the observations turn out during execution, the time-points whose labels are consistent with those observations have all been executed, and the constraints whose labels are consistent with those observations have all been satisfied. The strategy is dynamic in that its execution decisions may react to observations. The original formulation of CSTNs included propositional labels only on time-points, but the DC-checking algorithm was impractical because it was based on a conversion of the semantic constraints into an exponentially-sized Disjunctive Temporal Network. Later work added propositional labels to temporal constraints, and yielded a sound-and-complete propagation-based DC-checking algorithm, empirically demonstrated to be practical across a variety of CSTNs. This paper introduces a streamlined version of a CSTN in which propositional labels may appear on constraints, but not on time-points. This change simplifies the definition of the DC property, as well as the propagation rules for the DC-checking algorithm. It also simplifies the proofs of the soundness and completeness of those rules. This paper provides two translations from traditional CSTNs to streamlined CSTNs. Each translation preserves the DC property and, for any DC network, ensures that any dynamic execution strategy for that network can be extended to a strategy for its streamlined counterpart. Finally, this paper presents an empirical comparison of two versions of the DC-checking algorithm: the original version and a simplified version for streamlined CSTNs. The comparison is based on CSTN benchmarks from earlier work. For small-sized CSTNs, the original version shows the best performance, but the performance difference between the two versions decreases as the number of time-points in the CSTN increases. We conclude that the simplified algorithm is a practical alternative for checking the dynamic consistency of CSTNs

Some results and challenges Extending Dynamic Controllability to Agile Controllability in Simple Temporal Networks with Uncertainties

Simple Temporal Networks with Uncertainty (STNU) are an expressive means to represent temporal constraints, requirements, or obligations. They feature contingent timepoints, which are set by the environment with a specified interval. Dynamic controllability is the current most relaxed notion for checking that the constraints are not in conflict. It requires that a timepoint may only depend on earlier timepoints. Agile controllability extends dynamic controllability by taking into account that a later timepoint might already be known earlier and allowing a timepoint to depend on all timepoints whose value is known before. In this report, we formally introduce the notion of an STNU with oracle timepoints, formally define the notion of agile controllability, and discuss approaches for checking agile controllability

Dynamic Controllability of Parameterized CSTNUs

A Conditional Simple Temporal Network with Uncertainty (CSTNU) models temporal constraint satisfaction problems in which the environment sets uncontrollable timepoints and conditions. The executor observes and reacts to such uncontrollable assignments as time advances with the CSTNU execution. However, there exist scenarios in which the occurrence of some future timepoints must be fixed as soon as the execution starts. We call these timepoints \textit{parameters}. For a correct execution, parameters must assume values that guarantee the possibility of satisfying all temporal constraints, whatever the environment decides the execution time for uncontrollable timepoints and the truth value of conditions, i.e., dynamic controllability (DC). Here, we formalize the extension of the CSTNU with parameters. Furthermore, we define a set of rules to check the DC of such extended CSTNU. These rules additionally solve the problem inverse to checking DC: computing restrictions on parameter values that yield DC guarantees. The proposed rules can be composed into a sound and complete procedure