arXiv subjects

Thomas M. Prinz

Publications and source records attributed to Thomas M. Prinz.

3 recordsLinked to original sources

arXiv2026

Deciding Reachability and the Covering Problem with Diagnostics for Sound Acyclic Free-Choice Workflow Nets

A central decision problem in Petri net theory is reachability asking whether a given marking can be reached from the initial marking. Related is the covering problem (or sub-marking reachbility), which decides whether there is a reachable marking covering at least the tokens in the given marking. For live and bounded free-choice nets as well as for sound free-choice workflow nets, both problems are polynomial in their computational complexity. This paper refines this complexity for the class of sound acyclic free-choice workflow nets to a quadratic polynomial, more specifically to $O(P^2 + T^2)$. Furthermore, this paper shows the feasibility of accurately explaining why a given marking is or is not reachable. This can be achieved by three new concepts: admissibility, maximum admissibility, and diverging transitions. Admissibility requires that all places in a given marking are pairwise concurrent. Maximum admissibility states that adding a marked place to an admissible marking would make it inadmissible. A diverging transition is a transition which originally "produces" the concurrent tokens that lead to a given marking. In this paper, we provide algorithms for all these concepts and explain their computation in detail by basing them on the concepts of concurrency and post-dominance frontiers - a well known concept from compiler construction. In doing this, we present straight-forward implementations for solving (sub-marking) reachability.

cs.FL↗

arXiv2024

Pushing the Limits: Concurrency Detection in Acyclic Sound Free-Choice Workflow Nets in $O(P^2 + T^2)$

Concurrency is an important aspect of Petri nets to describe and simulate the behavior of complex systems. Knowing which places and transitions could be executed in parallel helps to understand nets and enables analysis techniques and the computation of other properties, such as causality, exclusivity, etc.. All techniques based on concurrency detection depend on the efficiency of this detection methodology. Kovalyov and Esparza have developed algorithms that compute all concurrent places in $O\big((P+T)TP^2\big)$ for live and bounded nets (where $P$ and $T$ are the numbers of places and transitions) and in $O\big(P(P+T)^2\big)$ for live and bounded free-choice nets. Although these algorithms have a reasonably good computational complexity, large numbers of concurrent pairs of nodes may still lead to long computation times. This paper complements the palette of concurrency detection algorithms with the Concurrent Paths (CP) algorithm for sound free-choice workflow nets. The algorithm allows parallelization and has a worst-case computational complexity of $O(P^2 + T^2)$ for acyclic nets and of $O(P^3 + PT^2)$ for cyclic nets. Although the computational complexity of cyclic nets has not improved, the evaluation shows the benefits of CP, especially, if the net contains many nodes in concurrency relation.

cs.DS↗

arXiv2024

How Participants Respond to Computer Delays

Reaction time studies with computers investigate how and how quickly participants respond to changing sensory input. They promise simple and precise measurement of time and inputs and offer interesting insights into human behavior. However, several previous studies have discovered imprecisions in timing appearing as delays, depending on the browser, software and programming used for conducting such studies. Since the accuaracy of the collected data is widely discussed, we aim to provide new results on the effect of unintended delays on participants' behavior. For this purpose, a new reaction time study was conducted. Computer delays were added to the experiment to investigate their effects on participants' performance and repulsion. Minimal changes in participants' behavior did occur and should be furtherly investigated, as the power of this study was rather low and might not have uncovered all underlying effects. The following report details our study design and results and offers several suggestions for improvements in further studies.

cs.HC↗