Optimal Conditional Reachability for Multi-priced Timed Automata

Abstract

In this paper, we prove decidability of the optimal conditional reachability problem for multi-priced timed automata, an extension of timed automata with multiple cost variables evolving according to given rates for each location. More precisely, we consider the problem of determining the minimal cost of reaching a given target state, with respect to some primary cost variable, while respecting upper bound constraints on the remaining (secondary) cost variables. Decidability is proven by constructing a zone-based algorithm that always terminates while synthesizing the optimal cost with a single secondary cost variable. The approach is then lifted to any number of secondary cost variables. 1 Variables with these two properties are sometimes referred to as observers in the literature.

A Nivat Theorem for Weighted Timed Automata and Weighted Relative Distance Logic

“…The ongoing research should extend the currently obtained results to ω-infinite words. This work should be further extended to the multi-weighted setting for WTA, e.g., the optimal reward-cost ratio [7,8] or the optimal consumption of several resources where some resources must be restricted [22]. A logical characterization of untimed multi-weighted automata was given in [15].…”

“…In the literature, various models of WTA were considered, e.g., linearly priced timed automata [3,4,21], multi-weighted timed automata with knapsack-problem objective [22], and WTA with measures like average, reward-cost ratio [7,8] and discounting [2,18,19]. In [24,25], WTA over semirings were studied with respect to the classical automata-theoretic questions.…”

Infinite Runs in Weighted Timed Automata with Energy Constraints

“…In these models-so-called priced or weighted timed automata-the cost can be used to measure the performance of a system allowing various optimization problems to be considered. Examples include cost-optimal reachability problem in a single-cost setting [2,3], as well as in a multi-cost setting [20], or the computation of (mean-cost or discounted) costoptimal infinite schedules [6,16]. Also games where players try to optimize the cost have been considered [1,7,13,5,10], and several model-checking problems have been studied [12,5,9,11].…”

Lower-bound-constrained runs in weighted timed automata

“…Weighted (or priced) timed automata [3], [2], [9] have emerged as a useful formalism for formulating a wide range of resource-allocation and optimization problems [4], [14], with applications in areas such as embedded systems [18]. In [10], a new class of resource-allocation problems was introduced, namely that of constructing infinite schedules subject to boundary constraints on the accumulation of resources.…”