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A Pattern-Based Formalization of Cloud-Based Elastic Systems Cloud-based elastic systems leverage cloud infrastructures to implement elasticity, the ability ofcomputing systems to dynamically adjust their capacity by changing the allocation of resources in response to fluctuating workloads. The runtime behavior of elastic systems is the result of an intricate interplay of many factors that include the input workload, the elasticity logic determining the resources allocation, and the technology of the underlying cloud. This makes elastic systems difficult to design and hard to specify. In this paper we propose a novel formalization of elasticity and related concepts that is based on timed patterns written using timed regular expressions. Timed regular expressions naturally deal with dense-time signals, and timed patterns allow us to intuitively describe relevant changes in those signals. This, in turn, enables us to directly characterize elasticity as relation between relevant changes in the input workload and in the resources allocation signals. We firstly characterize the relevant changes by means of timed patterns, and then we define desired and undesired behaviors of cloud-based elastic systems in terms of the occurrence of such patterns over an observation period.