Quantitative Monitor Automata

Chatterjee, Krishnendu; Henzinger, Thomas A.; Otop, Jan

doi:10.1007/978-3-662-53413-7_2

Cited by 14 publications

(10 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although such properties have been studied much in the context of probabilistic model checking [2], decision problems in verification [31], and games with quantitative objectives [32], [33], in runtime verification, we observe a gap. While some formalisms for monitoring certain quantitative properties have been proposed [12], [34], [35], to the best of our knowledge, our work is the first general semantic framework that explores what it means to monitor and approximate generic quantitative properties of traces. We believe that such a framework is needed for the systematic study of precision-resource trade-offs in runtime verification.…”

Section: Related Workmentioning

confidence: 99%

Quantitative and Approximate Monitoring

Henzinger¹,

Ege²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

In runtime verification, a monitor watches a trace of a system and, if possible, decides after observing each finite prefix whether or not the unknown infinite trace satisfies a given specification. We generalize the theory of runtime verification to monitors that attempt to estimate numerical values of quantitative trace properties (instead of attempting to conclude boolean values of trace specifications), such as maximal or average response time along a trace. Quantitative monitors are approximate: with every finite prefix, they can improve their estimate of the infinite trace's unknown property value. Consequently, quantitative monitors can be compared with regard to a precisioncost trade-off: better approximations of the property value require more monitor resources, such as states (in the case of finite-state monitors) or registers, and additional resources yield better approximations. We introduce a formal framework for quantitative and approximate monitoring, show how it conservatively generalizes the classical boolean setting for monitoring, and give several precision-cost trade-offs for monitors. For example, we prove that there are quantitative properties for which every additional register improves monitoring precision.

show abstract

Section: Related Workmentioning

confidence: 99%

Quantitative and Approximate Monitoring

Henzinger¹,

Ege²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…This offline algorithm is based on the syntax trees of signal regular expressions, and it is difficult to extend for online monitoring. Weighted automata are used for quantitative monitoring in [CHO16,JBG + 18,JBGN18], but the time model was discrete.…”

Section: Algorithm By Zonesmentioning

confidence: 99%

Online Quantitative Timed Pattern Matching with Semiring-Valued Weighted Automata

Waga

2019

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Monitoring of a signal plays an essential role in the runtime verification of cyber-physical systems. Qualitative timed pattern matching is one of the mathematical formulations of monitoring, which gives a Boolean verdict for each sub-signal according to the satisfaction of the given specification. There are two orthogonal directions of extension of the qualitative timed pattern matching. One direction on the result is quantitative: what engineers want is often not a qualitative verdict but the quantitative measurement of the satisfaction of the specification. The other direction on the algorithm is online checking: the monitor returns some verdicts before obtaining the entire signal, which enables to monitor a running system. It is desired from application viewpoints. In this paper, we conduct these two extensions, taking an automata-based approach. This is the first quantitative and online timed pattern matching algorithm to the best of our knowledge. More specifically, we employ what we call timed symbolic weighted automata to specify quantitative specifications to be monitored, and we obtain an online algorithm using the shortest distance of a weighted variant of the zone graph and dynamic programming. Moreover, our problem setting is semiring-based and therefore, general. Our experimental results confirm the scalability of our algorithm for specifications with a time-bound.

show abstract

“…Finally, we consider the case of the threshold λ = 0. The case of an arbitrary threshold λ ∈ Q can be easily reduced to the case λ = 0 (see [9,8] for intuitions and techniques in mean-payoff games a.k.a. limit-average games).…”

Section: The Regular Average-value Problemmentioning

confidence: 99%

“…Quantitative asymptotic bounds for polynomial-time termination in VASS have also been studied [4,26], however, these works do not consider long-run average property. Finally, a related model of automata with monitor counters with long-run average property have been considered in [9,8]. However, there are some crucial differences: in automata with monitor counters, the cost always depends on one counter, and counters are reset once the value is used.…”

Section: Introductionmentioning

confidence: 99%

Long-Run Average Behavior of Vector Addition Systems with States

Chatterjee,

Henzinger,

Otop

2019

Preprint

Self Cite

View full text Add to dashboard Cite

A vector addition system with states (VASS) consists of a finite set of states and counters. A configuration is a state and a value for each counter; a transition changes the state and each counter is incremented, decremented, or left unchanged. While qualitative properties such as state and configuration reachability have been studied for VASS, we consider the long-run average cost of infinite computations of VASS. The cost of a configuration is for each state, a linear combination of the counter values. In the special case of uniform cost functions, the linear combination is the same for all states. The (regular) long-run emptiness problem is, given a VASS, a cost function, and a threshold value, if there is a (lasso-shaped) computation such that the long-run average value of the cost function does not exceed the threshold. For uniform cost functions, we show that the regular long-run emptiness problem is (a) decidable in polynomial time for integer-valued VASS, and (b) decidable but nonelementarily hard for natural-valued VASS (i.e., nonnegative counters). For general cost functions, we show that the problem is (c) NP-complete for integer-valued VASS, and (d) undecidable for natural-valued VASS. Our most interesting result is for (c) integer-valued VASS with general cost functions, where we establish a connection between the regular long-run emptiness problem and quadratic Diophantine inequalities. The general (nonregular) long-run emptiness problem is equally hard as the regular problem in all cases except (c), where it remains open.

show abstract

Quantitative Monitor Automata

Cited by 14 publications

References 27 publications

Quantitative and Approximate Monitoring

Quantitative and Approximate Monitoring

Online Quantitative Timed Pattern Matching with Semiring-Valued Weighted Automata

Long-Run Average Behavior of Vector Addition Systems with States

Contact Info

Product

Resources

About