Sound and Complete Algorithms for Checking the Dynamic Controllability of Temporal Networks with Uncertainty, Disjunction and Observation

Abstract

Temporal networks are data structures for representing and reasoning about temporal constraints on activities. Many kinds of temporal networks have been defined in the literature, differing in their expressiveness. The simplest kinds of networks have polynomial algorithms for determining their consistency or controllability, but corresponding algorithms for more expressive networks (e.g., those that include observation nodes or disjunctive constraints) have so far been unavailable. However, recent work has introduced a new approach to such algorithms based on translating temporal networks into Timed Game Automata (TGAs) and then using off-the-shelf software to synthesize execution strategies-or determine that none exist. So far, that approach has only been used on Simple Temporal Networks with Uncertainty, for which polynomial algorithms already exist. This paper extends the temporal-network-to-TGA approach to accommodate observation nodes and disjunctive constraints. Insodoing the paper presents, for the first time, sound and complete algorithms for checking the dynamic controllability of these more expressive networks. The translations also highlight the theoretical relationships between various kinds of temporal networks and the TGA model. The new algorithms have immediate applications in the workflow models being developed to automate business processes, including in the health-care domain.

Efficient execution of dynamically controllable simple temporal networks with uncertainty

“…One of the main goals of this paper is to provide such a proof. This is done in two steps: (1) proving that an STNU that has an SRN loop must not be dynamically controllable; and (2) proving that an STNU without any SRN loops must be dynamically controllable. The first step is addressed in this section, the second step in the next section.…”

“…Base cases P(0) and P (1). Since G has no SRN loops, the initial AllMax graph, (G * x ) 0 , cannot have any negative loops.…”

“…Although that work does not provide faster DC-checking algorithms for STNUs, it has subsequently been extended to provide the first sound-and-complete DC-checking algorithm for a much wider class of temporal networks that allow disjunctive constraints and constraints conditioned on real-time observation of boolean propositions [1].…”

“…They presented an algorithm, called FastIDC, for solving the IDC problem, but did not prove its completeness. 1 In 2013, Nilsson et al [22] showed that the FastIDC algorithm was, in fact, not complete by presenting a counter-example. They fixed the problem and proved that the modified algorithm was complete by showing that it was equivalent to the MMV-01 algorithm.…”

Complexity bounds for the controllability of temporal networks with conditions, disjunctions, and uncertainty

“…The computational complexities of many of the simpler temporal models have been well-studied, but the same cannot be said of more advanced models. Despite this gap, there has been considerable effort put into constructing improved algorithms for these feature-rich temporal networks [3,4,5,10,24]. Figure 1: A taxonomic organization of temporal networks considered in this paper, how they relate to one another, and the complexity classes to which their decision problems belong.…”