arXiv subjects

Sarah Winkler

Publications and source records attributed to Sarah Winkler.

At least 19 recordsLinked to original sources

arXiv2026

Monitoring Data-aware Temporal Properties (Extended Version)

Dynamic systems in AI are often complex and heterogeneous, so that an internal specification is not accessible and verification techniques such as model checking are not applicable. Monitoring is in such cases an attractive alternative, as it evaluates desirable properties along traces generated by an unknown dynamic system. In this work, we consider anticipatory monitoring of linear-time properties enriched with an arbitrary SMT theory over finite traces (LTLfMT). Anticipatory monitoring in this setting is highly challenging, as the monitoring state depends on both the trace prefix seen so far and all its possible finite continuations. Under reasonable assumptions on the background theory, we present and formally prove the correctness of a novel foundational framework for monitoring properties in an expressive fragment of LTLfMT. The framework combines automata-theoretic methods to handle the temporal aspects of the logic, with automated reasoning techniques to address the first-order dimension. Moreover, we identify for the first time decidable fragments of this monitoring problem that are practically relevant as they combine linear arithmetic with uninterpreted functions, which covers e.g. data-aware business processes and dynamic systems operating over a read-only database. Feasibility is witnessed by a prototype implementation and preliminary evaluation.

cs.AI↗

arXiv2026

Detecting Dynamic Relationships in Object-Centric Event Logs

Object-centric process mining examines how processes interact with multiple co-evolving objects, and has gained great interest in recent years. However, object-centric event logs (OCELs) leave object relationships underspecified in several respects, especially if relationships are dynamic, i.e., they change over time. In this paper, we identify and formally define for the first time assumptions that allow to represent and manipulate dynamic relationships in OCELs in a semantically unambiguous way. We evaluate existing logs to show that our assumptions are often satisfied, ensuring full transparency of relationship semantics.

cs.DB↗

arXiv2025

First-Order LTLf Synthesis with Lookback (Extended Version)

Reactive synthesis addresses the problem of generating a controller for a temporal specification in an adversarial environment; it was typically studied for LTL. Driven by applications ranging from AI to business process management, LTL modulo first order-theories over finite traces (LTLfMT) has recently gained traction, where propositional variables in properties are replaced by first-order constraints. Though reactive synthesis for LTLf with some first-order features has been addressed, existing work in this direction strongly restricts or excludes the possibility to compare variables across instants, a limitation that severely restricts expressiveness and applicability. In this work we present a reactive synthesis procedure for LTLfMT, where properties support "lookback" to model cross-instant comparison of variables. Our procedure works for full LTLfMT with lookback, subsuming the fragments of LTLfMT for which realizability was studied earlier. However, the setting with cross-instant comparison is inherently highly complex, as realizability is undecidable even over decidable background theories. Hence termination of our approach is in general not guaranteed. Nevertheless, we prove its soundness, and show that it is complete if a bound on the strategy length exists. Finally, we show that our approach constitutes a decision procedure for several relevant fragments of LTLfMT, at once re-proving known decidability results and identifying new decidable classes.

cs.LO↗

arXiv2025

To bind or not to bind? Discovering Stable Relationships in Object-centric Processes (Extended Version)

Object-centric process mining investigates the intertwined behavior of multiple objects in business processes. From object-centric event logs, object-centric Petri nets (OCPN) can be discovered to replay the behavior of processes accessing different object types. Although they indicate how objects flow through the process and co-occur in events, OCPNs remain underspecified about the relationships of objects. Hence, they are not able to represent synchronization, i.e. executing objects only according to their intended relationships, and fail to identify violating executions. Existing formal modeling approaches, such as object-centric Petri nets with identifiers (OPID), represent object identities and relationships to synchronize them correctly. However, OPID discovery has not yet been studied. This paper uses explicit data models to bridge the gap between OCPNs and formal OPIDs. We identify the implicit assumptions of stable many-to-one relationships in object-centric event logs, which implies synchronization of related objects. To formally underpin this observation, we combine OCPNs with explicit stable many-to-one relationships in a rigorous mapping from OCPNs to OPIDs explicitly capturing the intended stable relationships and the synchronization of related objects. We prove that the original OCPNs and the resulting OPIDs coincide for those executions that satisfy the intended relationships. Moreover, we provide an implementation of the mapping from OCPN to OPID under stable relationships.

cs.LO↗

arXiv2025

Efficient Conformance Checking of Rich Data-Aware Declare Specifications (Extended)

Despite growing interest in process analysis and mining for data-aware specifications, alignment-based conformance checking for declarative process models has focused on pure control-flow specifications, or mild data-aware extensions limited to numerical data and variable-to-constant comparisons. This is not surprising: finding alignments is computationally hard, even more so in the presence of data dependencies. In this paper, we challenge this problem in the case where the reference model is captured using data-aware Declare with general data types and data conditions. We show that, unexpectedly, it is possible to compute data-aware optimal alignments in this rich setting, enjoying at once efficiency and expressiveness. This is achieved by carefully combining the two best-known approaches to deal with control flow and data dependencies when computing alignments, namely A* search and SMT solving. Specifically, we introduce a novel algorithmic technique that efficiently explores the search space, generating descendant states through the application of repair actions aiming at incrementally resolving constraint violations. We prove the correctness of our algorithm and experimentally show its efficiency. The evaluation witnesses that our approach matches or surpasses the performance of the state of the art while also supporting significantly more expressive data dependencies, showcasing its potential to support real-world applications.

cs.DB↗

arXiv2025

Object-centric Processes with Structured Data and Exact Synchronization (Extended Version)

Real-world processes often involve interdependent objects that also carry data values, such as integers, reals, or strings. However, existing process formalisms fall short to combine key modeling features, such as tracking object identities, supporting complex datatypes, handling dependencies among them, and object-aware synchronization. Object-centric Petri nets with identifiers (OPIDs) partially address these needs but treat objects as unstructured identifiers (e.g., order and item IDs), overlooking the rich semantics of complex data values (e.g., item prices or other attributes). To overcome these limitations, we introduce data-aware OPIDs (DOPIDs), a framework that strictly extends OPIDs by incorporating structured data manipulation capabilities, and full synchronization mechanisms. In spite of the expressiveness of the model, we show that it can be made operational: Specifically, we define a novel conformance checking approach leveraging satisfiability modulo theories (SMT) to compute data-aware object-centric alignments.

cs.MA↗

arXiv2024

Femtosecond laser written waveguides in sapphire for visible light delivery

A promising solution for scalable integrated optics of trapped-ion quantum processors are curved waveguides guiding visible light within sapphire bulk material. To the best of our knowledge, no curved waveguides were investigated in sapphire so far, and no measurements of waveguides with visible light in undoped planar sapphire substrates were reported. Here, we demonstrate femtosecond laser writing of depressed cladding waveguides in sapphire. Laser parameters, such as pulse energy, pulse duration, and repetition rate, as well as waveguide geometry parameters, were optimized to guide 728 nm light. This resulted in single-mode waveguides with a propagation loss of 1.9(3) dB/cm. The investigation of curved waveguides showed a sharp increase in total loss for curvature radii below 15 mm. Our results demonstrate the potential of femtosecond laser writing as a powerful technique for creating integrated optical waveguides in the volume of sapphire substrates. Such waveguides could be a building block for integrated optics in trapped-ion quantum processors.

physics.optics↗

arXiv2024

Object-Centric Conformance Alignments with Synchronization (Extended Version)

Real-world processes operate on objects that are inter-dependent. To accurately reflect the nature of such processes, object-centric process mining techniques are needed, notably conformance checking. However, while the object-centric perspective has recently gained traction, few concrete process mining techniques have been presented so far. Moreover, existing approaches are severely limited in their abilities to keep track of object identity and object dependencies. Consequently, serious problems in logs remain undetected. In this paper, we present a new formalism that combines the key modelling features of two existing approaches, in particular the ability of object-centric Petri nets to capture one-to-many relations and the one of Petri nets with identifiers to compare and synchronize objects based on their identity. We call the resulting formalism 'object-centric Petri nets with identifiers', and define alignments and the conformance checking task for this setting. We propose a conformance checking approach for such nets based on an encoding in satisfiability modulo theories (SMT), and illustrate how it can be effectively used to overcome shortcomings of earlier work. To assess its practicality, we perform an evaluation on data from the literature.

cs.LO↗

arXiv2023

Linear-Time Verification of Data-Aware Processes Modulo Theories via Covers and Automata (Extended Version)

The need to model and analyse dynamic systems operating over complex data is ubiquitous in AI and neighboring areas, in particular business process management. Analysing such data-aware systems is a notoriously difficult problem, as they are intrinsically infinite-state. Existing approaches work for specific datatypes, and/or limit themselves to the verification of safety properties. In this paper, we lift both such limitations, studying for the first time linear-time verification for so-called data-aware processes modulo theories (DMTs), from the foundational and practical point of view. The DMT model is very general, as it supports processes operating over variables that can store arbitrary types of data, ranging over infinite domains and equipped with domain-specific predicates. Specifically, we provide four contributions. First, we devise a semi-decision procedure for linear-time verification of DMTs, which works for a very large class of datatypes obeying to mild model-theoretic assumptions. The procedure relies on a unique combination of automata-theoretic and cover computation techniques to respectively deal with linear-time properties and datatypes. Second, we identify an abstract, semantic property that guarantees the existence of a faithful finite-state abstraction of the original system, and show that our method becomes a decision procedure in this case. Third, we identify concrete, checkable classes of systems that satisfy this property, generalising several results in the literature. Finally, we present an implementation and a first experimental evaluation.

cs.LO↗

arXiv2023

Decidable Fragments of LTLf Modulo Theories (Extended Version)

We study Linear Temporal Logic Modulo Theories over Finite Traces (LTLfMT), a recently introduced extension of LTL over finite traces (LTLf) where propositions are replaced by first-order formulas and where first-order variables referring to different time points can be compared. In general, LTLfMT was shown to be semi-decidable for any decidable first-order theory (e.g., linear arithmetics), with a tableau-based semi-decision procedure. In this paper we present a sound and complete pruning rule for the LTLfMT tableau. We show that for any LTLfMT formula that satisfies an abstract, semantic condition, that we call finite memory, the tableau augmented with the new rule is also guaranteed to terminate. Last but not least, this technique allows us to establish novel decidability results for the satisfiability of several fragments of LTLfMT, as well as to give new decidability proofs for classes that are already known.

cs.AI↗

arXiv2022

Monitoring Arithmetic Temporal Properties on Finite Traces

We study monitoring of linear-time arithmetic properties against finite traces generated by an unknown dynamic system. The monitoring state is determined by considering at once the trace prefix seen so far, and all its possible finite-length, future continuations. This makes monitoring at least as hard as satisfiability and validity. Traces consist of finite sequences of assignments of a fixed set of variables to numerical values. Properties are specified in a logic we call ALTLf, combining LTLf (LTL on finite traces) with linear arithmetic constraints that may carry lookahead, i.e., variables may be compared over multiple instants of the trace. While the monitoring problem for this setting is undecidable in general, we show decidability for (a) properties without lookahead, and (b) properties with lookahead that satisfy the abstract, semantic condition of finite summary, studied before in the context of model checking. We then single out concrete, practically relevant classes of constraints guaranteeing finite summary. Feasibility is witnessed by a prototype implementation.

cs.LO↗

arXiv2022

Conformance Checking with Uncertainty via SMT (Extended Version)

Logs of real-life processes often feature uncertainty pertaining the recorded timestamps, data values, and/or events. We consider the problem of checking conformance of uncertain logs against data-aware reference processes. Specifically, we show how to solve it via SMT encodings, lifting previous work on data-aware SMT-based conformance checking to this more sophisticated setting. Our approach is modular, in that it homogeneously accommodates for different types of uncertainty. Moreover, using appropriate cost functions, different conformance checking tasks can be addressed. We show the correctness of our approach and witness feasibility through a proof-of-concept implementation.

cs.AI↗

arXiv2022

CTL* model checking for data-aware dynamic systems with arithmetic

The analysis of complex dynamic systems is a core research topic in formal methods and AI, and combined modelling of systems with data has gained increasing importance in applications such as business process management. In addition, process mining techniques are nowadays used to automatically mine process models from event data, often without correctness guarantees. Thus verification techniques for linear and branching time properties are needed to ensure desired behavior. Here we consider data-aware dynamic systems with arithmetic (DDSAs), which constitute a concise but expressive formalism of transition systems with linear arithmetic guards. We present a CTL* model checking procedure for DDSAs that relies on a finite-state abstraction by means of a set of formulas that capture variable configurations. Linear-time verification was shown to be decidable in specific classes of DDSAs where the constraint language or the control flow are suitably confined. We investigate several of these restrictions for the case of CTL*, with both positive and negative results: CTL* verification is proven decidable for monotonicity and integer periodicity constraint systems, but undecidable for feedback free and bounded lookback systems. To demonstrate the feasibility of our approach, we implemented it in the SMT-based prototype ada, showing that many practical business process models can be effectively analyzed.

cs.LO↗

arXiv2022

Soundness of Data-Aware Processes with Arithmetic Conditions

Data-aware processes represent and integrate structural and behavioural constraints in a single model, and are thus increasingly investigated in business process management and information systems engineering. In this spectrum, Data Petri nets (DPNs) have gained increasing popularity thanks to their ability to balance simplicity with expressiveness. The interplay of data and control-flow makes checking the correctness of such models, specifically the well-known property of soundness, crucial and challenging. A major shortcoming of previous approaches for checking soundness of DPNs is that they consider data conditions without arithmetic, an essential feature when dealing with real-world, concrete applications. In this paper, we attack this open problem by providing a foundational and operational framework for assessing soundness of DPNs enriched with arithmetic data conditions. The framework comes with a proof-of-concept implementation that, instead of relying on ad-hoc techniques, employs off-the-shelf established SMT technologies. The implementation is validated on a collection of examples from the literature, and on synthetic variants constructed from such examples.

cs.LO↗

arXiv2022

Linear-Time Verification of Data-Aware Dynamic Systems with Arithmetic

Combined modeling and verification of dynamic systems and the data they operate on has gained momentum in AI and in several application domains. We investigate the expressive yet concise framework of data-aware dynamic systems (DDS), extending it with linear arithmetic, and provide the following contributions. First, we introduce a new, semantic property of "finite summary", which guarantees the existence of a faithful finite-state abstraction. We rely on this to show that checking whether a witness exists for a linear-time, finite-trace property is decidable for DDSs with finite summary. Second, we demonstrate that several decidability conditions studied in formal methods and database theory can be seen as concrete, checkable instances of this property. This also gives rise to new decidability results. Third, we show how the abstract, uniform property of finite summary leads to modularity results: a system enjoys finite summary if it can be partitioned appropriately into smaller systems that possess the property. Our results allow us to analyze systems that were out of reach in earlier approaches. Finally, we demonstrate the feasibility of our approach in a prototype implementation.

cs.LO↗

arXiv2021

CoCoMoT: Conformance Checking of Multi-Perspective Processes via SMT (Extended Version)

Conformance checking is a key process mining task for comparing the expected behavior captured in a process model and the actual behavior recorded in a log. While this problem has been extensively studied for pure control-flow processes, conformance checking with multi-perspective processes is still at its infancy. In this paper, we attack this challenging problem by considering processes that combine the data and control-flow dimensions. In particular, we adopt data Petri nets (DPNs) as the underlying reference formalism, and show how solid, well-established automated reasoning techniques can be effectively employed for computing conformance metrics and data-aware alignments. We do so by introducing the CoCoMoT (Computing Conformance Modulo Theories) framework, with a fourfold contribution. First, we show how SAT-based encodings studied in the pure control-flow setting can be lifted to our data-aware case, using SMT as the underlying formal and algorithmic framework. Second, we introduce a novel preprocessing technique based on a notion of property-preserving clustering, to speed up the computation of conformance checking outputs. Third, we provide a proof-of-concept implementation that uses a state-of-the-art SMT solver and report on preliminary experiments. Finally, we discuss how CoCoMoT directly lends itself to a number of further tasks, like multi- and anti-alignments, log analysis by clustering, and model repair.

cs.AI↗

arXiv2020

Runtime Complexity Analysis of Logically Constrained Rewriting

Logically constrained rewrite systems (LCTRSs) are a versatile and efficient rewriting formalism that can be used to model programs from various programming paradigms, as well as simplification systems in compilers and SMT solvers. In this paper, we investigate techniques to analyse the worst-case runtime complexity of LCTRSs. For that, we exploit synergies between previously developed decomposition techniques for standard term rewriting by Avanzini et al. in conjunction with alternating time and size bound approximations for integer programs by Brockschmidt et al. and adapt these techniques suitably to LCTRSs. Furthermore, we provide novel modularization techniques to exploit loop bounds from recurrence equations which yield sublinear bounds. We have implemented the method in TCT to test the viability of our method.

cs.CC↗

arXiv2020

Tools in Term Rewriting for Education

Term rewriting is a Turing complete model of computation. When taught to students of computer science, key properties of computation as well as techniques to analyze programs on an abstract level are conveyed. This paper gives a swift introduction to term rewriting and presents several automatic tools to analyze term rewrite systems which were developed by the Computational Logic Group at the University of Innsbruck. These include the termination tool TTT2, the confluence prover CSI, the completion tools mkbTT and KBCV, the complexity tool TcT, the strategy tool AutoStrat, as well as FORT, an implementation of the decision procedure for the first-order theory for a decidable class of rewrite systems. Besides its applications in research, this software pool has also proved invaluable for teaching, e.g., in multiple editions of the International Summer School on Rewriting.

cs.LO↗