Using finite transducers for describing and synthesising structural time-series constraints

Abstract

International audienceWe describe a large family of constraints for structural time series by means of function composition. These constraints are on aggregations of features of patterns that occur in a time series, such as the number of its peaks, or the range of its steepest ascent. The patterns and features are usually linked to physical properties of the time series generator, which are important to capture in a constraint model of the system, i.e. a conjunction of constraints that produces similar time series. We formalise the patterns using finite transducers, whose output alphabet corresponds to semantic values that precisely describe the steps for identifying the occurrences of a pattern. Based on that description, we automatically synthesise automata with accumulators, as well as constraint checkers. The description scheme not only unifies the structure of the existing 30 time-series constraints in the Global Constraint Catalogue, but also leads to over 600 new constraints, with more than 100,000 lines of synthesised code

Systematic Derivation of Bounds and Glue Constraints for Time-Series Constraints

“…The reverse of its time series X is X = 0, 2, 2, 2, 2, 2, 2, 0, 0, 4, 7, 4, 4, 2, 0, 0, 4, 4 and has the signature S mir = '<=====>=<<>=>>=<=', which we will call the mirror of the original signature S. The automaton of Figure 2 returns the same value whether it consumes a signature or its mirror: the peaks of X are the reverses of the peaks of X and the aggregation of their feature values is the same because all the operators φ f and φ g are commutative. We have this property for 19 of the 20 regular expressions in [5]. The idea now is to derive an implied constraint, which we will call a glue constraint, between the three accumulator triples of such an automaton after it has consumed (i) a signature w, (ii) a prefix w 1 of w, and (iii) the mirror of the corresponding suffix w 2 of w. For instance, let us split S into the prefix P = '=>=<<=<' and the suffix T = '>>=<=====>', which has the mirror T mir = '<=====>=<<'.…”

“…In this paper, we introduce parametric glue constraints and show that they can be derived automatically for time-series constraints, which we introduced a year later in [5].…”

“…This pair of feature/aggregator makes sense for 18 of the 20 regular expressions in [5]. Our goal is to derive an upper bound on the maximum of the minima of all σ-patterns in a time series, where σ is any of those regular expressions.…”

“…In [5], we showed how to synthesise a deterministic finite automaton, enriched with accumulators [7], from any triple σ, f, g that specifies a time-series constraint. We now discuss the required background concepts using an example, namely the regular expression Peak = '<(<|=)*(>|=)*>' of Example 1.…”

“…It is currently unknown how to maintain domain consistency efficiently on such constraints. We propose parametric ways of systematically deriving glue constraints, which are a particular kind of implied constraints, as well as aggregation bounds that can be added to the decomposition of time-series constraints [5]. We evaluate the beneficial propagation impact of the derived implied constraints and bounds, both alone and together.…”