Executing Discrete/Continuous Declarative Process Specifications via Complex Event Processing

Traditional Business Process Management (BPM) focuses on discrete events and fails to incorporate critical continuous sensor data in cyber-physical environments. Hybrid declarative specifications, utilizing Signal Temporal Logic (STL), address this limitation by allowing constraints over both discrete events and real-valued signals. However, existing work has been limited to monitoring and post-hoc conformance checking. This paper introduces a novel execution architecture based on Complex Event Processing (CEP) that enables the realtime execution and enforcement of hybrid declarative models. Our three-layer approach integrates STL-inspired predicates into the execution flow, allowing the system to actively trigger activities and enforce process boundaries based on continuous sensor behavior. This approach bridges the gap between hybrid specification and operational control.

Our main contributions are:

1 The term hybrid in this context has been introduced in [8].

2 We extend the execution paradigm of declarative process models from purely discrete event data to hybrid event–signal scenarios.

3 We present a CEP-based execution architecture capable of evaluating STLinspired predicates and constraints in real time.

4 We show how hybrid declarative constraints can be enforced during execution, enabling reactive and proactive behavior in data-rich environments.

The paper describes the architecture as a three-layer runtime:

1 Atomic Event Layer (L1): This layer is responsible for normalizing input streams and transforming them into semantically meaningful data tokens. It handles two primary input types: (i) discrete atomic events, representing the completion of business activities, and (ii) continuous signal samples, representing time-stamped telemetry measurements. Each atomic event is described as a tuple e = ⟨caseId, activity, ts⟩. Continuous input is represented as s = ⟨caseId, sensorId, value, timestamp⟩. Relational filtering predicates evaluate incoming metrics against static signal boundaries to broadcast binary state-change tokens categorized as ACTIVATION or TARGET signals.

2 Constraint Status Layer (L2): This layer is the Constraint-Level Pattern Matching Layer (Complex Event Processing). It is a stateless stream processor that detects temporal patterns defining a constraint’s logic. It consumes the stream of standardized activation and target tokens from L1 and maps sequential lifecycle shifts through pattern queries for each constraint template, such as those derived from STL. For example, a Response constraint's fulfillment is detected by a pattern that identifies a valid target token following an activation within a given time window, or violations are detected using negative patterns with timeouts.

3 Process Status Layer (L3): This layer builds on the lifecycle milestones emitted by the pattern-matching layer and provides a stateful view of execution for each unique process case. Its primary role is twofold: (i) to manage and aggregate the status of all individual constraints into an overall case-level picture, and (ii) to trigger processlevel actions whenever significant state changes occur. It interprets lifecycle milestones to maintain active process state vectors, dynamically computing allowed subsequent operations (Task Enablement) and trace-wide validity (Instance Finishability), rendering the current permissible actions transparently visible.

The architecture functions as a continuous, reactive dataflow pipeline: events are ingested and normalized in L1, complex patterns are detected in L2, and lifecycle events are interpreted to manage process state and trigger actions in L3. The execution engine acts as a dynamic state-space constraint filter, computing two real-time state vectors: (i) Task Enablement, which defines the exact subset of activities that an operator is permitted to perform, and (ii) Instance Finishability, which determines whether the cumulative process trace satisfies all mandatory constraints. This enables genuine realtime constraint evaluation in settings where processes must react to continuous sensor streams.

The paper demonstrates feasibility on resource-constrained edge devices, achieving sub-millisecond latency at typical IoT event rates while maintaining stable resource consumption. The evaluation confirms that hybrid declarative process execution is feasible on edge devices, addressing the core research gap of moving from post-hoc conformance checking to active runtime enforcement. The architecture successfully handles hybrid Declare templates, including unary, binary, and correlation-based constraints with both forward and backward temporal directionality. For actual process execution, when an STL threshold activation or a discrete task transition occurs, the process layer intercepts the lifecycle state change and translates it into an event-driven trigger. This allows the system to invoke external APIs or inject automated activity updates. The enforcement mechanisms are demonstrated through an interactive process dashboard where operators can see which tasks are currently executable based on constraint states and trace history, and constraints can be configured with an auto-execute flag, triggering target tasks directly in response to signal changes. The evaluation confirms that the overhead of embedding real-time signal analysis remains within the operational bounds of edge control loops.

The expressiveness analysis validates that the translation from STL to EPL introduces no loss of expressiveness, covering all behavioral categories: Atemporal Unary Structures (Existence and NotExistence), Forward-Looking Binary Structures (Response and Chain Response), Backward-Looking Historical Structures (Precedence), and Multi-Perspective Data-Correlated Structures. The system preserves the expressiveness of the hybrid declarative paradigm. The scalability analysis confirms that the architecture scales efficiently for realistic IoT workloads, with median end-to-end processing latency remaining below 0.1 ms at typical IoT event rates, confirming sub-millisecond response times consistent with linear scaling on edge devices. Furthermore, deployment on actual IoT hardware confirmed negligible overhead and sustained throughput far exceeding typical industrial sensor frequencies without requiring cloud offloading or distributed infrastructure. The overall evaluation confirms that hybrid declarative process execution is feasible on resource-constrained edge devices, addressing the core research gap of moving from post-hoc conformance checking to active runtime enforcement.

The paper concludes by stating: Overall, the evaluation confirms that hybrid declarative process execution is feasible on edge devices, addressing the core research gap of moving from post-hoc conformance checking to active runtime enforcement. Future work will extend this architecture toward autonomous process control by leveraging STL robustness for graded, non-binary enforcement and by integrating machine learning techniques for predictive adaptation in distributed IoT/CPS environments. The paper's structure is organized as follows: Section 2 covers declarative modeling, STL, and the principles of CEP as a stream reasoning paradigm. Section 3 introduces our core contribution: the three-layer hybrid execution architecture and an implementation-independent mapping of hybrid constraints to CEP logic. Section 4 describes the working prototype built on the Esper engine. Section 5 assesses expressiveness and scalability. Section 6 discusses related work, and Section 7 concludes with future research directions.

Table 2 summarizes how traditional discrete Declare templates are lifted into continuous-time STL semantics [9], abstracted via intermediate Denotational Complex Event Logic (CEL) expressions, and operationalized into concrete Esper EPL [15]. Table 3 specifies this decomposition by demonstrating how first-order data-driven predicates and crossevent data relationships (φc (x, y)) are managed across the runtime pipeline. The final step in L1 transforms these raw events into semantic atomic events in a unified constraintStatus stream, which serves as the input for L2 and contains all activations and targets relevant for constraint monitoring.

The execution model differs from traditional imperative process enactment by acting as a dynamic state-space constraint filter, computing two real-time state vectors: (i) Task Enablement, which defines the exact subset of activities that an operator is permitted to perform, and (ii) Instance Finishability, which determines whether the cumulative process trace satisfies all mandatory constraints. This allows the system to inform users if a task is entirely forbidden or only allowed under specific payload conditions. The three layers operate as a continuous, reactive dataflow pipeline: events are ingested and normalized in L1, complex patterns are detected in L2, and lifecycle events are interpreted to manage process state and trigger actions in L3. All logic is expressed as continuous EPL queries and event-driven callbacks, enabling low-latency monitoring and control. The architecture successfully handles hybrid Declare templates, including unary, binary, and correlation-based constraints with both forward and backward temporal directionality."

The paper's core contribution is: "We extend the execution paradigm of declarative process models from purely discrete event data to hybrid event–signal scenarios. We present a CEP-based execution architecture capable of evaluating STLinspired predicates and constraints in real time. We show how hybrid declarative constraints can be enforced during execution, enabling reactive and proactive behavior in data-rich environments. The paper's conclusion is: This paper bridges the gap between the specification of hybrid declarative constraints and their execution, enabling the development of next-generation processaware systems that are both context-sensitive and sensor-integrated."

The evaluation confirms that hybrid declarative process execution is feasible on edge devices, achieving sub-millisecond latency at typical IoT event rates while maintaining stable resource consumption. The results show that the three-layer architecture scales efficiently for realistic IoT workloads. At event rates from 100 to 10,000 EPS, average CPU utilization scaled linearly from 0.9% to 14.4%, while memory consumption remained stable between 434 and 489 MB. Median end-to-end processing latency remained below 0.1 ms, with P99 values under 0.5 ms, confirming sub-millisecond response times consistent with linear scaling."

The paper's final sentence is: meeting a critical requirement for IoT process control: genuine real-time constraint evaluation and enforcement. The paper's summary of its architecture is that it bridges the gap between hybrid declarative specifications and operational control by introducing a CEP-based execution architecture for STL-enriched process models.

The summary provided in the paper is: "This paper bridges the gap between hybrid declarative process specifications and operational control by introducing a CEP-based execution architecture for STL-enriched process models. Traditional declarative approaches have largely been limited to monitoring and post hoc conformance checking of hybrid traces, whereas our three-layer architecture enables real-time enforcement of constraints on both discrete events and continuous signals. By transforming STL-inspired predicates into CEP patterns, the system actively triggers activities and enforces process boundaries based on sensor behavior, extending declarative execution from purely discrete scenarios into IoT environments."

The paper's final sentence is: This paper bridges the gap between hybrid declarative specifications and operational control, enabling the development of next-generation processaware systems that are both context-sensitive and sensor-integrated.

The summary provided in the paper is: "This paper bridges the gap between hybrid declarative specifications and operational control by introducing a CEP-based execution architecture for STL-enriched process models. Traditional declarative approaches have largely been limited to monitoring and post hoc conformance checking of hybrid traces, whereas our three-layer architecture enables real-time enforcement of constraints on both discrete events and continuous signals. By transforming STL-inspired predicates into CEP patterns, the system actively triggers activities and enforces process boundaries based on sensor behavior, extending declarative execution from purely discrete scenarios into IoT environments."

The summary provided in the paper is: "This paper bridges the gap between hybrid declarative specifications and operational control by introducing a CEP-based execution architecture for STL-enriched process models. Traditional declarative approaches have largely been limited to monitoring and post hoc conformance checking of hybrid traces, whereas our three-layer architecture enables real-time enforcement of constraints on both discrete events and continuous signals. By transforming STL-inspired predicates into CEP patterns, the system actively triggers activities and enforces process boundaries based on sensor behavior, extending declarative execution from purely discrete scenarios into

Here are the specific improvements that can be made to AI systems based on this research, and what these improved systems will be capable of doing:

1. The integration of a CEP-based execution engine (using Esper) with Signal Temporal Logic (STL) predicates allows for the creation of Process-Aware Agents.

2. These agents can perform real-time, proactive control in cyber-physical systems by enforcing constraints that span both discrete events (e.g., task completion) and continuous sensor data (e.g., temperature, pressure).

Specific Capabilities:

1. The AI system can automatically trigger physical or software activities based on continuous signal thresholds and durations—a capability traditional discrete BPM or standard monitoring systems lack.

2. It can proactively enforce safety boundaries in dynamic environments, such as stopping a chemical reaction if the temperature exceeds a threshold for too long, or starting cooling procedures within a specific time window of that breach.

3. The system can manage complex state-space constraints (like precedence rules) to ensure sequential operations only occur when continuous conditions (e.g., temperature stability) are met for the required duration, preventing unsafe actions like restarting a machine during critical phases.

4. It can dynamically enable or disable specific tasks based on the current constraint status, presenting operators with a real-time view of what actions are permissible and why (e.g., displaying a tooltip explaining that a Restart task is blocked because the required 20-second cooling duration has not yet passed).

5. The system can operate efficiently on resource-constrained edge devices (like Raspberry Pi) with low latency (sub-millisecond response times), making real-time constraint enforcement practical for industrial IoT and shop-floor control.

In essence, this research moves AI from merely monitoring what happened to actively driving and controlling processes in real time based on the continuous state of the physical environment.

Traditional Business Process Management (BPM) focuses on discrete events and fails to incorporate critical continuous sensor data in cyber-physical environments. Hybrid declarative specifications, utilizing Signal Temporal Logic (STL), address this limitation by allowing constraints over both discrete events and real-valued signals. However, existing work has been limited to monitoring and post-hoc conformance checking. This paper introduces a novel execution architecture based on Complex Event Processing (CEP) that enables the real-time execution and enforcement of hybrid declarative models. Our three-layer approach integrates STL-inspired predicates into the execution flow, allowing the system to actively trigger activities and enforce process boundaries based on continuous sensor behavior. This approach bridges the gap between hybrid specification and operational control.