arXiv subjects

Landon Taylor

Publications and source records attributed to Landon Taylor.

5 recordsLinked to original sources

arXiv2026

RAGTIMER 1.0: Rapid Rare-Event Partial State Space Construction for Stochastic VAS (extended version)

Transient reachability analysis of rare events in Continuous-Time Stochastic Vector Addition Systems (CTSVAS) such as Chemical Reaction Networks (CRNs) has proven a formidable challenge to cutting-edge tools. Underlying a CTSVAS is a continuous-time Markov chain (CTMC), and CTMC transient reachability analysis calls for Probabilistic Model Checking (PMC). This analysis requires the explicit representation of a model's entire state space. Rare events occur with extremely low probability, compounding the challenge of probabilistic analysis. In CRNs, it is imperative to verify the probability of rare events; even a low concentration of a species can have pathological consequences. This paper presents the RAGTIMER 1.0 tool, which efficiently builds a partial state space for a CTSVAS by enumerating traces to a rare event of interest and expanding them to exploit concurrency and cycles, providing a guaranteed lower bound on the probability of a rare event. Guaranteed lower bounds are particularly useful in synthetic biological applications because they indicate how and when a rare event can be experimentally observed. RAGTIMER is an attractive alternative to existing rare event analysis methods for CTSVAS models. It outperforms existing PMC tools and refutes multiple probability estimates from rare-event stochastic simulation on multiple challenging CRN models. RAGTIMER uses optimized data structures, a simple input format, and memory-safe Rust code to improve the scalability and accessibility of PMC for industry professionals.

cs.FL↗

arXiv2025

Prefix Trees Improve Memory Consumption in Large-Scale Continuous-Time Stochastic Models

Highly-concurrent system models with vast state spaces like Chemical Reaction Networks (CRNs) that model biological and chemical systems pose a formidable challenge to cutting-edge formal analysis tools. Although many symbolic approaches have been presented, transient probability analysis of CRNs, modeled as Continuous-Time Markov Chains (CTMCs), requires explicit state representation. For that purpose, current cutting-edge methods use hash maps, which boast constant average time complexity and linear memory complexity. However, hash maps often suffer from severe memory limitations on models with immense state spaces. To address this, we propose using prefix trees to store states for large, highly concurrent models (particularly CRNs) for memory savings. We present theoretical analyses and benchmarks demonstrating the favorability of prefix trees over hash maps for very large state spaces. Additionally, we propose using a Bounded Model Checking (BMC) pre-processing step to impose a variable ordering to further improve memory usage along with preliminary evaluations suggesting its effectiveness. We remark that while our work is motivated primarily by the challenges posed by CRNs, it is generalizable to all CTMC models.

cs.DS↗

arXiv2025

Reasoning about Rare-Event Reachability in Stochastic Vector Addition Systems via Affine Vector Spaces

Rare events in Stochastic Vector Addition System (VAS) are of significant interest because, while extremely unlikely, they may represent undesirable behavior that can have adverse effects. Their low probabilities and potentially extremely large state spaces challenge existing probabilistic model checking and stochastic rare-event simulation techniques. In particular, in Chemical Reaction Networks (CRNs), a chemical kinetic language often represented as VAS, rare event effects may be pathological. We present two novel heuristics for priority-first partial state space expansion and trace generation tuned to the transient analysis of rare-event probability in VAS: Iterative Subspace Reduction (ISR) and Single Distance Priority (SDP). Both methods construct a closed vector space containing all solution states. SDP then simply prioritizes shorter distances to this ``solution space'', while ISR constructs a set of nested subspaces, where short and highly-probable satisfying traces are likely to pass through in sequence. The resulting partial state graph from each method contains likely traces to rare-event states, allowing efficient probabilistic model checking to compute a lower-bound probability of a rare event of interest. These methods are deterministic, fast, and demonstrate marked performance on challenging CRN models.

cs.FL↗

arXiv2024

Characteristics of Powerful Radio Galaxies

Mature radio galaxies such as M87 belong to a specific subclass of active galaxies (AGN) whose evolution in time endows them with five distinguishing characteristics, including (1) low excitation emission, (2) low star formation rates, (3) high bulge stellar-velocity dispersion, (4) bright stellar nuclei, and (5) weak or nonexistent merger signatures. We show how to understand these seemingly disparate characteristics as originating from the time evolution of powerful radio quasars and describe a new model prediction that tilted accretion disks in AGN are expected to occur in bright quasars but not in other subclasses of AGN. The picture we present should be understood as the most compelling evidence for counter-rotation as a key element in feedback from accreting black holes.

astro-ph.HE↗

arXiv2024

Tools at the Frontiers of Quantitative Verification

The analysis of formal models that include quantitative aspects such as timing or probabilistic choices is performed by quantitative verification tools. Broad and mature tool support is available for computing basic properties such as expected rewards on basic models such as Markov chains. Previous editions of QComp, the comparison of tools for the analysis of quantitative formal models, focused on this setting. Many application scenarios, however, require more advanced property types such as LTL and parameter synthesis queries as well as advanced models like stochastic games and partially observable MDPs. For these, tool support is in its infancy today. This paper presents the outcomes of QComp 2023: a survey of the state of the art in quantitative verification tool support for advanced property types and models. With tools ranging from first research prototypes to well-supported integrations into established toolsets, this report highlights today's active areas and tomorrow's challenges in tool-focused research for quantitative verification.

cs.LO↗