Cumulative-Time Signal Temporal Logic Article Swipe

PDF

Hongkai Chen , Z. Zhang , Shouvik Roy , Ezio Bartocci , Scott A. Smolka , Scott D. Stoller , Shan Lin ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2504.10325

Signal Temporal Logic (STL) is a widely adopted specification language in cyber-physical systems for expressing critical temporal requirements, such as safety conditions and response time. However, STL's expressivity is not sufficient to capture the cumulative duration during which a property holds within an interval of time. To overcome this limitation, we introduce Cumulative-Time Signal Temporal Logic (CT-STL) that operates over discrete-time signals and extends STL with a new cumulative-time operator. This operator compares the sum of all time steps for which its nested formula is true with a threshold. We present both a qualitative and a quantitative (robustness) semantics for CT-STL and prove both their soundness and completeness properties. We provide an efficient online monitoring algorithm for both semantics. Finally, we show the applicability of CT-STL in two case studies: specifying and monitoring cumulative temporal requirements for a microgrid and an artificial pancreas.

Related Topics

The Signal (2014 Film)

Wow! Signal

Signal (Software)

Max Headroom Signal Hijacking

Signal (South Korean Tv Series)

Signal Processing

Thumb Signal

United States Army Signal Corps

Quantization (Signal Processing)

Digital Signal Processor

Mobile Phone Signal

The Signal And The Noise

Concepts

No concepts available.

Metadata

Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2504.10325
PDF: https://arxiv.org/pdf/2504.10325
OA Status: green
OpenAlex ID: https://openalex.org/W4415160672

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W4415160672

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.48550/arxiv.2504.10325

Digital Object Identifier
Title: Cumulative-Time Signal Temporal Logic

Work title
Type: preprint

OpenAlex work type
Language: en

Primary language
Publication year: 2025

Year of publication
Publication date: 2025-04-14

Full publication date if available
Authors: Hongkai Chen, Z. Zhang, Shouvik Roy, Ezio Bartocci, Scott A. Smolka, Scott D. Stoller, Shan Lin

List of authors in order
Landing page: https://arxiv.org/abs/2504.10325

Publisher landing page
PDF URL: https://arxiv.org/pdf/2504.10325

Direct link to full text PDF
Open access: Yes

Whether a free full text is available
OA status: green

Open access status per OpenAlex
OA URL: https://arxiv.org/pdf/2504.10325

Direct OA link when available
Cited by: 0

Total citation count in OpenAlex

Full payload

id	https://openalex.org/W4415160672
doi	https://doi.org/10.48550/arxiv.2504.10325
ids.doi	https://doi.org/10.48550/arxiv.2504.10325
ids.openalex	https://openalex.org/W4415160672
fwci
type	preprint
title	Cumulative-Time Signal Temporal Logic
biblio.issue
biblio.volume
biblio.last_page
biblio.first_page
topics[0].id	https://openalex.org/T10142
topics[0].field.id	https://openalex.org/fields/17
topics[0].field.display_name	Computer Science
topics[0].score	0.8999999761581421
topics[0].domain.id	https://openalex.org/domains/3
topics[0].domain.display_name	Physical Sciences
topics[0].subfield.id	https://openalex.org/subfields/1703
topics[0].subfield.display_name	Computational Theory and Mathematics
topics[0].display_name	Formal Methods in Verification
topics[1].id	https://openalex.org/T11010
topics[1].field.id	https://openalex.org/fields/17
topics[1].field.display_name	Computer Science
topics[1].score	0.8776000142097473
topics[1].domain.id	https://openalex.org/domains/3
topics[1].domain.display_name	Physical Sciences
topics[1].subfield.id	https://openalex.org/subfields/1702
topics[1].subfield.display_name	Artificial Intelligence
topics[1].display_name	Logic, Reasoning, and Knowledge
topics[2].id	https://openalex.org/T10215
topics[2].field.id	https://openalex.org/fields/17
topics[2].field.display_name	Computer Science
topics[2].score	0.8389999866485596
topics[2].domain.id	https://openalex.org/domains/3
topics[2].domain.display_name	Physical Sciences
topics[2].subfield.id	https://openalex.org/subfields/1702
topics[2].subfield.display_name	Artificial Intelligence
topics[2].display_name	Semantic Web and Ontologies
is_xpac	False
apc_list
apc_paid
language	en
locations[0].id	pmh:oai:arXiv.org:2504.10325
locations[0].is_oa	True
locations[0].source.id	https://openalex.org/S4306400194
locations[0].source.issn
locations[0].source.type	repository
locations[0].source.is_oa	True
locations[0].source.issn_l
locations[0].source.is_core	False
locations[0].source.is_in_doaj	False
locations[0].source.display_name	arXiv (Cornell University)
locations[0].source.host_organization	https://openalex.org/I205783295
locations[0].source.host_organization_name	Cornell University
locations[0].source.host_organization_lineage	https://openalex.org/I205783295
locations[0].license	cc-by
locations[0].pdf_url	https://arxiv.org/pdf/2504.10325
locations[0].version	submittedVersion
locations[0].raw_type	text
locations[0].license_id	https://openalex.org/licenses/cc-by
locations[0].is_accepted	False
locations[0].is_published	False
locations[0].raw_source_name
locations[0].landing_page_url	http://arxiv.org/abs/2504.10325
locations[1].id	doi:10.48550/arxiv.2504.10325
locations[1].is_oa	True
locations[1].source.id	https://openalex.org/S4306400194
locations[1].source.issn
locations[1].source.type	repository
locations[1].source.is_oa	True
locations[1].source.issn_l
locations[1].source.is_core	False
locations[1].source.is_in_doaj	False
locations[1].source.display_name	arXiv (Cornell University)
locations[1].source.host_organization	https://openalex.org/I205783295
locations[1].source.host_organization_name	Cornell University
locations[1].source.host_organization_lineage	https://openalex.org/I205783295
locations[1].license	cc-by
locations[1].pdf_url
locations[1].version
locations[1].raw_type	article
locations[1].license_id	https://openalex.org/licenses/cc-by
locations[1].is_accepted	False
locations[1].is_published
locations[1].raw_source_name
locations[1].landing_page_url	https://doi.org/10.48550/arxiv.2504.10325
indexed_in	arxiv, datacite
authorships[0].author.id	https://openalex.org/A5101397369
authorships[0].author.orcid	https://orcid.org/0000-0001-7206-6584
authorships[0].author.display_name	Hongkai Chen
authorships[0].author_position	first
authorships[0].raw_author_name	Chen, Hongkai
authorships[0].is_corresponding	False
authorships[1].author.id	https://openalex.org/A5083264017
authorships[1].author.orcid
authorships[1].author.display_name	Z. Zhang
authorships[1].author_position	middle
authorships[1].raw_author_name	Zhang, Zeyu
authorships[1].is_corresponding	False
authorships[2].author.id	https://openalex.org/A5088384753
authorships[2].author.orcid
authorships[2].author.display_name	Shouvik Roy
authorships[2].author_position	middle
authorships[2].raw_author_name	Roy, Shouvik
authorships[2].is_corresponding	False
authorships[3].author.id	https://openalex.org/A5050836932
authorships[3].author.orcid	https://orcid.org/0000-0002-8004-6601
authorships[3].author.display_name	Ezio Bartocci
authorships[3].author_position	middle
authorships[3].raw_author_name	Bartocci, Ezio
authorships[3].is_corresponding	False
authorships[4].author.id	https://openalex.org/A5039202410
authorships[4].author.orcid	https://orcid.org/0000-0002-7348-630X
authorships[4].author.display_name	Scott A. Smolka
authorships[4].author_position	middle
authorships[4].raw_author_name	Smolka, Scott A.
authorships[4].is_corresponding	False
authorships[5].author.id	https://openalex.org/A5021474885
authorships[5].author.orcid	https://orcid.org/0000-0002-8824-6835
authorships[5].author.display_name	Scott D. Stoller
authorships[5].author_position	middle
authorships[5].raw_author_name	Stoller, Scott D.
authorships[5].is_corresponding	False
authorships[6].author.id	https://openalex.org/A5003166096
authorships[6].author.orcid	https://orcid.org/0000-0001-6362-2972
authorships[6].author.display_name	Shan Lin
authorships[6].author_position	last
authorships[6].raw_author_name	Lin, Shan
authorships[6].is_corresponding	False
has_content.pdf	True
has_content.grobid_xml	True
is_paratext	False
open_access.is_oa	True
open_access.oa_url	https://arxiv.org/pdf/2504.10325
open_access.oa_status	green
open_access.any_repository_has_fulltext	False
created_date	2025-10-14T00:00:00
display_name	Cumulative-Time Signal Temporal Logic
has_fulltext	True
is_retracted	False
updated_date	2025-11-06T06:51:31.235846
primary_topic.id	https://openalex.org/T10142
primary_topic.field.id	https://openalex.org/fields/17
primary_topic.field.display_name	Computer Science
primary_topic.score	0.8999999761581421
primary_topic.domain.id	https://openalex.org/domains/3
primary_topic.domain.display_name	Physical Sciences
primary_topic.subfield.id	https://openalex.org/subfields/1703
primary_topic.subfield.display_name	Computational Theory and Mathematics
primary_topic.display_name	Formal Methods in Verification
cited_by_count	0
locations_count	2
best_oa_location.id	pmh:oai:arXiv.org:2504.10325
best_oa_location.is_oa	True
best_oa_location.source.id	https://openalex.org/S4306400194
best_oa_location.source.issn
best_oa_location.source.type	repository
best_oa_location.source.is_oa	True
best_oa_location.source.issn_l
best_oa_location.source.is_core	False
best_oa_location.source.is_in_doaj	False
best_oa_location.source.display_name	arXiv (Cornell University)
best_oa_location.source.host_organization	https://openalex.org/I205783295
best_oa_location.source.host_organization_name	Cornell University
best_oa_location.source.host_organization_lineage	https://openalex.org/I205783295
best_oa_location.license	cc-by
best_oa_location.pdf_url	https://arxiv.org/pdf/2504.10325
best_oa_location.version	submittedVersion
best_oa_location.raw_type	text
best_oa_location.license_id	https://openalex.org/licenses/cc-by
best_oa_location.is_accepted	False
best_oa_location.is_published	False
best_oa_location.raw_source_name
best_oa_location.landing_page_url	http://arxiv.org/abs/2504.10325
primary_location.id	pmh:oai:arXiv.org:2504.10325
primary_location.is_oa	True
primary_location.source.id	https://openalex.org/S4306400194
primary_location.source.issn
primary_location.source.type	repository
primary_location.source.is_oa	True
primary_location.source.issn_l
primary_location.source.is_core	False
primary_location.source.is_in_doaj	False
primary_location.source.display_name	arXiv (Cornell University)
primary_location.source.host_organization	https://openalex.org/I205783295
primary_location.source.host_organization_name	Cornell University
primary_location.source.host_organization_lineage	https://openalex.org/I205783295
primary_location.license	cc-by
primary_location.pdf_url	https://arxiv.org/pdf/2504.10325
primary_location.version	submittedVersion
primary_location.raw_type	text
primary_location.license_id	https://openalex.org/licenses/cc-by
primary_location.is_accepted	False
primary_location.is_published	False
primary_location.raw_source_name
primary_location.landing_page_url	http://arxiv.org/abs/2504.10325
publication_date	2025-04-14
publication_year	2025
referenced_works_count	0
abstract_inverted_index.a	5, 38, 66, 87, 92, 95, 137
abstract_inverted_index.To	46
abstract_inverted_index.We	89, 109
abstract_inverted_index.an	42, 111, 140
abstract_inverted_index.as	19
abstract_inverted_index.in	10, 126
abstract_inverted_index.is	4, 28, 84
abstract_inverted_index.of	44, 75, 124
abstract_inverted_index.to	31
abstract_inverted_index.we	50, 120
abstract_inverted_index.STL	64
abstract_inverted_index.all	76
abstract_inverted_index.and	22, 62, 94, 101, 106, 131, 139
abstract_inverted_index.for	13, 79, 99, 116, 136
abstract_inverted_index.its	81
abstract_inverted_index.new	67
abstract_inverted_index.not	29
abstract_inverted_index.sum	74
abstract_inverted_index.the	33, 73, 122
abstract_inverted_index.two	127
abstract_inverted_index.This	70
abstract_inverted_index.both	91, 103, 117
abstract_inverted_index.case	128
abstract_inverted_index.over	59
abstract_inverted_index.show	121
abstract_inverted_index.such	18
abstract_inverted_index.that	57
abstract_inverted_index.this	48
abstract_inverted_index.time	77
abstract_inverted_index.true	85
abstract_inverted_index.with	65, 86
abstract_inverted_index.(STL)	3
abstract_inverted_index.Logic	2, 55
abstract_inverted_index.STL's	26
abstract_inverted_index.holds	40
abstract_inverted_index.prove	102
abstract_inverted_index.steps	78
abstract_inverted_index.their	104
abstract_inverted_index.time.	24, 45
abstract_inverted_index.which	37, 80
abstract_inverted_index.CT-STL	100, 125
abstract_inverted_index.Signal	0, 53
abstract_inverted_index.during	36
abstract_inverted_index.nested	82
abstract_inverted_index.online	113
abstract_inverted_index.safety	20
abstract_inverted_index.widely	6
abstract_inverted_index.within	41
abstract_inverted_index.adopted	7
abstract_inverted_index.capture	32
abstract_inverted_index.extends	63
abstract_inverted_index.formula	83
abstract_inverted_index.present	90
abstract_inverted_index.provide	110
abstract_inverted_index.signals	61
abstract_inverted_index.systems	12
abstract_inverted_index.(CT-STL)	56
abstract_inverted_index.Finally,	119
abstract_inverted_index.However,	25
abstract_inverted_index.Temporal	1, 54
abstract_inverted_index.compares	72
abstract_inverted_index.critical	15
abstract_inverted_index.duration	35
abstract_inverted_index.interval	43
abstract_inverted_index.language	9
abstract_inverted_index.operates	58
abstract_inverted_index.operator	71
abstract_inverted_index.overcome	47
abstract_inverted_index.property	39
abstract_inverted_index.response	23
abstract_inverted_index.studies:	129
abstract_inverted_index.temporal	16, 134
abstract_inverted_index.algorithm	115
abstract_inverted_index.efficient	112
abstract_inverted_index.introduce	51
abstract_inverted_index.microgrid	138
abstract_inverted_index.operator.	69
abstract_inverted_index.pancreas.	142
abstract_inverted_index.semantics	98
abstract_inverted_index.soundness	105
abstract_inverted_index.artificial	141
abstract_inverted_index.conditions	21
abstract_inverted_index.cumulative	34, 133
abstract_inverted_index.expressing	14
abstract_inverted_index.monitoring	114, 132
abstract_inverted_index.semantics.	118
abstract_inverted_index.specifying	130
abstract_inverted_index.sufficient	30
abstract_inverted_index.threshold.	88
abstract_inverted_index.limitation,	49
abstract_inverted_index.properties.	108
abstract_inverted_index.qualitative	93
abstract_inverted_index.(robustness)	97
abstract_inverted_index.completeness	107
abstract_inverted_index.expressivity	27
abstract_inverted_index.quantitative	96
abstract_inverted_index.requirements	135
abstract_inverted_index.applicability	123
abstract_inverted_index.discrete-time	60
abstract_inverted_index.requirements,	17
abstract_inverted_index.specification	8
abstract_inverted_index.cyber-physical	11
abstract_inverted_index.Cumulative-Time	52
abstract_inverted_index.cumulative-time	68
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	7
citation_normalized_percentile