Alignment-driven Event Checking (ADEC)

• ADEC is a framework that defines event checking via explicit alignments between observed event sequences and reference process models.
• It employs various strategies like synchronous, log, and model moves to diagnose deviations in full traces and fragments, including online and timed settings.
• The approach advances practical conformance by integrating repair strategies, uncertainty handling, and learned or external semantics to improve event-driven verification.

Searching arXiv for recent and foundational papers on alignment-based event checking, conformance checking, timed alignments, fragment alignments, and event-driven consistency. Alignment-driven Event Checking (ADEC) can be understood as a family of methods that use alignments, repaired traces, alignment-aware representations, or consistency witnesses to determine whether an observed event sequence, temporal fragment, or execution is plausible with respect to a reference process model, event class, or cyber-physical semantics. Across the literature, the idea appears in declarative process conformance, timed alignment, uncertain and stochastic logs, fragment-based conformance, online prefix checking, event-driven program verification, and alignment-aware event detection, even though these works do not present a single canonical formalization under one shared name (Casas-Ramos et al., 13 Mar 2025, Chatain et al., 2022, Bogdanov et al., 2022, Schuster et al., 2022, Zhou et al., 2022, Abdulla et al., 11 Aug 2025, Abbasnejad et al., 2015).

1. Conceptual scope

ADEC is best treated as an umbrella over several alignment regimes rather than as one fixed algorithm. In the process-mining lineage, the core object is an alignment between an observed trace and a model execution, usually expressed through synchronous, log, and model moves. In timed conformance checking, the alignment becomes a sequence of timestamp-edit moves such as stamp, delay, or mixed moves. In uncertain-log settings, the alignment is computed not against one deterministic trace but against a realization space or a stochastic trace model. In cyber-physical and event-driven software settings, the checking problem shifts toward whether observed transitions or partial traces can be aligned with external events, mailbox semantics, or shared-memory causality (Chatain et al., 2022, Bogdanov et al., 2022, Pegoraro et al., 2020, Cheng et al., 2018, Abdulla et al., 11 Aug 2025).

Setting	Alignment object	Checking question	Representative work
Process conformance	Trace-model move sequence	Which observed or missing events explain non-conformance?	(Casas-Ramos et al., 13 Mar 2025)
Timed conformance	Timestamp-edit sequence	Is deviation local, propagated, or mixed?	(Rino et al., 2022)
Uncertain logs	Realization-aware alignment	Is behavior conformant under uncertainty?	(Pegoraro et al., 2020)
Fragment checking	Infix/postfix alignment	Can a partial trace fit somewhere or complete correctly?	(Schuster et al., 2022)
Event-driven execution	Consistency witness	Can the candidate trace be realized legally?	(Abdulla et al., 11 Aug 2025)
Alignment-aware detection	Learned temporal warp or event stabilization	Does the sequence align under temporal uncertainty?	(Abbasnejad et al., 2015)

This suggests that ADEC is unified less by domain than by a recurrent operation: infer the closest, most plausible, or semantically legal alignment between observed events and a reference structure, then use that alignment as the checking artifact.

2. Structural alignment over traces and fragments

In declarative conformance checking, the alignment is a sequence of legal moves $(a_L,a_M)$ with $a_L \in A_L \cup \{\gg\}$ and $a_M \in A_M \cup \{\gg\}$. Synchronous moves consume the next trace activity if executing it does not permanently violate any DECLARE constraint, log moves skip an observed event, and model moves insert an activity whose execution does not permanently violate the model. An alignment is optimal when the total cost is minimized under the standard convention that asynchronous moves cost $1$ and synchronous moves cost $0$ (Casas-Ramos et al., 13 Mar 2025). In ADEC terms, this yields a direct event-level diagnosis: an event is either accepted, ignored as extra behavior, or compensated by inserting a missing model event.

Fragment-oriented work generalizes this beyond complete traces. Complete alignment requires replay from initial to final marking; prefix alignment permits an intermediate end state; infix alignment allows both start and end at reachable intermediate markings; postfix alignment allows an arbitrary reachable start but requires completion to the final marking. Formally, an infix alignment of a fragment $\sigma$ allows

$$(N,m_i)\rightsquigarrow (N,m_1)\xrightarrow{{}^*_2(\gamma)_{\downarrow_T}}(N,m_2)\rightsquigarrow (N,m_f),$$

whereas postfix alignment requires

$$(N,m_i)\rightsquigarrow (N,m_1)\xrightarrow{{}^*_2(\gamma)_{\downarrow_T}}(N,m_f)$$

for reachable $m_1,m_2$ (Schuster et al., 2022). This is central for ADEC whenever the checked object is not a full case trace but a stage-specific segment, a sliding window, or a tail fragment.

Online checking pushes the same idea into streaming settings. IWS maintains, for each active case, a set of prefix-alignment states

$$s=(n,\hat{\gamma},\hat{\sigma},\delta(\hat{\gamma}),dt)$$

inside a state buffer

$a_L \in A_L \cup \{\gg\}$0

and updates these states event by event using synchronous, log, and model moves over a trie built from proxy behavior (Zhou et al., 2022). This does not change the semantics of ADEC; it changes the operational regime from offline exact search to approximate incremental maintenance of alignment explanations.

3. Timed and uncertainty-aware event checking

Timed alignment turns event checking from a purely structural problem into a timestamp-aware repair problem. A timed observation is a sequence in

$a_L \in A_L \cup \{\gg\}$1

and the timed conformance problem asks for the valid execution of a timed model closest to that observation. The foundational timed-alignment work distinguishes two atomic temporal edits. A stamp move changes the timestamp of one event only; a delay move changes that event and all of its causal descendants. These induce two solved metrics: $a_L \in A_L \cup \{\gg\}$2, which is Manhattan distance on timestamp vectors, and $a_L \in A_L \cup \{\gg\}$3, which is Manhattan distance on causal delay or flow vectors (Chatain et al., 2022). The distinction is diagnostic: the same temporal discrepancy can be interpreted either as several isolated timestamp errors or as one upstream delay with downstream consequences.

Mixed moves extend that semantics. A mixed move is defined as

$a_L \in A_L \cup \{\gg\}$4

with cost

$a_L \in A_L \cup \{\gg\}$5

It permits one event’s timestamp error to decompose into a local correction $a_L \in A_L \cup \{\gg\}$6 and a propagated suffix shift $a_L \in A_L \cup \{\gg\}$7. For sequential process models, the optimal conforming trace is obtained by projecting each observed local duration $a_L \in A_L \cup \{\gg\}$8 onto its legal interval: $a_L \in A_L \cup \{\gg\}$9 The paper proves that this $a_M \in A_M \cup \{\gg\}$0 also minimizes $a_M \in A_M \cup \{\gg\}$1 over all $a_M \in A_M \cup \{\gg\}$2, and both distance computation and alignment construction are linear time in the trace length (Rino et al., 2022). For ADEC, this gives a concrete timestamp-checking operator that can classify a deviation as local, propagated, or mixed.

Uncertainty-aware work adds a different axis. For strongly uncertain event data, uncertainty over activity, timestamp, and event indeterminacy induces a realization set rather than one trace. The behavior-net construction compiles this realization set into a Petri-net language satisfying

$a_M \in A_M \cup \{\gg\}$3

so an alignment between the model and the behavior net computes the exact lower bound

$a_M \in A_M \cup \{\gg\}$4

on conformance cost (Pegoraro et al., 2020). For stochastically known logs, the stochastic trace model and stochastic synchronous product make synchronous moves probability-sensitive: a synchronous move on a label with probability $a_M \in A_M \cup \{\gg\}$5 receives cost

$a_M \in A_M \cup \{\gg\}$6

while model and log moves retain cost $a_M \in A_M \cup \{\gg\}$7 (Bogdanov et al., 2022). In ADEC terms, this means that a match supported only by an unlikely event interpretation is no longer treated as a free explanation.

4. Alignment as a learned or external semantics

ADEC is not confined to explicit process models. In efficient video event detection, alignment becomes a learned representation over variable-length temporal signals. A sequence $a_M \in A_M \cup \{\gg\}$8 is scored by a linear detector

$a_M \in A_M \cup \{\gg\}$9

where the descriptor

$1$0

uses an average $1$1 over DTW-derived deformation matrices harvested from positive pairs (Abbasnejad et al., 2015). Rather than committing to one canonical temporal normalization, the method averages over empirical alignments, yielding a fixed-dimensional descriptor that preserves chronology and supports linear detection. A plausible ADEC interpretation is that the system checks a candidate event against an alignment distribution distilled from valid examples.

In cyber-physical systems, the reference semantics may be the physical context that is supposed to justify software behavior. Orpheus instantiates this with an event-aware finite-state automaton

$1$2

so that some program transitions are valid only if the corresponding physical or external events are present (Cheng et al., 2018). Here ADEC is not comparing a log to a Petri net; it is checking whether an event-dependent runtime transition is semantically licensed by the world state. The same conceptual pattern appears: alignment between observed execution and its expected enabling events is the basis of anomaly detection.

A computer-vision variant appears in event cameras. For a region of interest $1$3, the method estimates the compensatory angular velocity

$1$4

that best stabilizes the event cloud inside that region, under a likelihood over warped event counts (Cai et al., 2024). Under the paper’s assumptions, compensatory rotational flow is inversely proportional to object distance. This is not process conformance, but it is alignment-driven event checking in a literal sense: a candidate physical hypothesis is accepted or rejected according to whether it aligns events into a coherent local structure.

5. Algorithmic regimes and computational landscape

The algorithmic profile of ADEC is heterogeneous because the underlying alignment objects differ. In timed conformance, the stamp-only distance $1$5 on general bounded time Petri nets can be solved as a convex or linear program with exponential worst-case complexity, while the specialized dynamic-programming algorithm for linear causal processes runs in

$1$6

and the delay-only algorithm on extended free choice time Petri nets runs in

$1$7

For mixed moves on sequential models, both distance computation and optimal alignment are linear time (Chatain et al., 2022, Rino et al., 2022). These results show that event-level temporal diagnosis can be efficient, but only under strong structural restrictions.

Fragment and online settings replace exact global search with structural pruning or approximation. For infix alignment, the advanced process-tree-based method substantially shortens overall computation time because the auxiliary WF-net contains fewer silent transitions, while all tested approaches yield infix alignments with identical costs (Schuster et al., 2022). IWS, in turn, achieves in some cases an order-of-magnitude faster execution time than the online prefix-alignment baseline, and in extreme cases finds prefix-alignments roughly three orders of magnitude faster, while maintaining event-by-event outputs through trie-based state updates (Zhou et al., 2022).

Declarative checking has recently shifted from automata- or planner-centric search to repair-centric A*. DECLAREALIGNER evaluates 8,054 synthetic and real-life alignment problems and reports an average time of $1$8 seconds for the final optimized variant, with 7,943 solved within a 5-minute limit and 7,014 instances on which it is the fastest algorithm. Its combined optimizations reduce the average number of expanded states from 3,802.7 to 109.7 and the average runtime from 101.6 seconds to 7.6 seconds (Casas-Ramos et al., 13 Mar 2025). For ADEC over DECLARE models, this is important because the alignment artifact remains optimal while the search is explicitly organized around violated activations and feasible repairs.

Event-driven software verification exposes a different computational boundary. Stateful DPOR for non-terminating event-driven applications reduced search space enough that 69 app pairs that did not finish without DPOR did finish and yielded a 7X average speedup (Trimananda et al., 2021). Event-DPOR proves correctness for all programs and optimality for a large subclass, while identifying that one redundancy-checking subproblem is NP-hard and addressing it with inexpensive incomplete tests (Abdulla et al., 2023). At the trace-consistency level, checking whether a candidate partial trace can be completed into a legal FIFO event-driven execution is NP-complete even when the number of handler threads is bounded, although the paper identifies a polynomial-time fragment in the absence of nested posting (Abdulla et al., 11 Aug 2025). These results locate a hard ADEC regime: when checking requires inferring hidden post/get correspondences, mailbox orders, and shared-memory consistency, the problem becomes fundamentally combinatorial.

6. Limitations, complementary metrics, and synthesis

The literature does not yet provide one unified ADEC formalism that jointly handles structural deviations, temporal uncertainty, probabilistic labels, partial observations, declarative constraints, and event-driven execution semantics. Timed alignment papers are strongest when the untimed part already matches and when the model class is restricted to linear causal processes, sequential process models, or extended free choice nets (Chatain et al., 2022, Rino et al., 2022). Fragment alignment can tell whether a subtrace fits somewhere in a process, but infix placement may remain ambiguous, and the best-performing method assumes block-structured workflow nets (Schuster et al., 2022). Online prefix methods such as IWS are approximate and depend on proxy-log quality, especially for permissive models with many silent transitions (Zhou et al., 2022). Behavior-net conformance gives an exact lower bound for strongly uncertain traces, but the upper bound still lacks an equally efficient dedicated construction (Pegoraro et al., 2020). Stochastic conformance addresses probability over activity labels, yet still assumes a deterministic process model and does not develop timestamp uncertainty (Bogdanov et al., 2022). DECLAREALIGNER is highly effective for declarative control-flow constraints, but it is presented for complete traces and future work is needed for data-aware models (Casas-Ramos et al., 13 Mar 2025).

A complementary line of work reverses the usual explanatory direction. Anti-alignments search not for the closest conforming explanation of an observed trace, but for model runs maximally far from the log. The loop-aware precision metric is

$1$9

so precision decreases when the model admits executions unsupported by observations (Chatain et al., 2019). This is not event-level checking in the usual ADEC sense, but it is useful as a complementary model-centric diagnostic: it identifies branches, loops, or activity patterns that the model can generate yet the log never exhibits.

A plausible synthesis is that ADEC is best viewed as a research program rather than a single method. Its recurring commitments are: observed events should be checked through an explicit alignment object; that object should make deviations interpretable as legal moves, repairs, or consistency witnesses; and algorithm design should exploit whatever structure the domain offers, whether that structure is causal time, declarative obligations, fragment locality, uncertainty models, event-dependent program semantics, or learned temporal deformation sets.