---
_id: '9646'
abstract:
- lang: eng
text: We consider the fundamental problem of deriving quantitative bounds on the
probability that a given assertion is violated in a probabilistic program. We
provide automated algorithms that obtain both lower and upper bounds on the assertion
violation probability. The main novelty of our approach is that we prove new and
dedicated fixed-point theorems which serve as the theoretical basis of our algorithms
and enable us to reason about assertion violation bounds in terms of pre and post
fixed-point functions. To synthesize such fixed-points, we devise algorithms that
utilize a wide range of mathematical tools, including repulsing ranking supermartingales,
Hoeffding's lemma, Minkowski decompositions, Jensen's inequality, and convex optimization.
On the theoretical side, we provide (i) the first automated algorithm for lower-bounds
on assertion violation probabilities, (ii) the first complete algorithm for upper-bounds
of exponential form in affine programs, and (iii) provably and significantly tighter
upper-bounds than the previous approaches. On the practical side, we show our
algorithms can handle a wide variety of programs from the literature and synthesize
bounds that are remarkably tighter than previous results, in some cases by thousands
of orders of magnitude.
acknowledgement: 'We are very thankful to the anonymous reviewers for the helpful
and valuable comments. The work was partially supported by the National Natural
Science Foundation of China (NSFC) Grant No. 61802254, the Huawei Innovation Research
Program, the ERC CoG 863818 (ForM-SMArt), the Facebook PhD Fellowship Program and
DOC Fellowship #24956 of the Austrian Academy of Sciences (ÖAW).'
article_processing_charge: No
author:
- first_name: Jinyi
full_name: Wang, Jinyi
last_name: Wang
- first_name: Yican
full_name: Sun, Yican
last_name: Sun
- first_name: Hongfei
full_name: Fu, Hongfei
id: 3AAD03D6-F248-11E8-B48F-1D18A9856A87
last_name: Fu
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Amir Kafshdar
full_name: Goharshady, Amir Kafshdar
id: 391365CE-F248-11E8-B48F-1D18A9856A87
last_name: Goharshady
orcid: 0000-0003-1702-6584
citation:
ama: 'Wang J, Sun Y, Fu H, Chatterjee K, Goharshady AK. Quantitative analysis of
assertion violations in probabilistic programs. In: Proceedings of the 42nd
ACM SIGPLAN International Conference on Programming Language Design and Implementation.
Association for Computing Machinery; 2021:1171-1186. doi:10.1145/3453483.3454102'
apa: 'Wang, J., Sun, Y., Fu, H., Chatterjee, K., & Goharshady, A. K. (2021).
Quantitative analysis of assertion violations in probabilistic programs. In Proceedings
of the 42nd ACM SIGPLAN International Conference on Programming Language Design
and Implementation (pp. 1171–1186). Online: Association for Computing Machinery.
https://doi.org/10.1145/3453483.3454102'
chicago: Wang, Jinyi, Yican Sun, Hongfei Fu, Krishnendu Chatterjee, and Amir Kafshdar
Goharshady. “Quantitative Analysis of Assertion Violations in Probabilistic Programs.”
In Proceedings of the 42nd ACM SIGPLAN International Conference on Programming
Language Design and Implementation, 1171–86. Association for Computing Machinery,
2021. https://doi.org/10.1145/3453483.3454102.
ieee: J. Wang, Y. Sun, H. Fu, K. Chatterjee, and A. K. Goharshady, “Quantitative
analysis of assertion violations in probabilistic programs,” in Proceedings
of the 42nd ACM SIGPLAN International Conference on Programming Language Design
and Implementation, Online, 2021, pp. 1171–1186.
ista: 'Wang J, Sun Y, Fu H, Chatterjee K, Goharshady AK. 2021. Quantitative analysis
of assertion violations in probabilistic programs. Proceedings of the 42nd ACM
SIGPLAN International Conference on Programming Language Design and Implementation.
PLDI: Programming Language Design and Implementation, 1171–1186.'
mla: Wang, Jinyi, et al. “Quantitative Analysis of Assertion Violations in Probabilistic
Programs.” Proceedings of the 42nd ACM SIGPLAN International Conference on
Programming Language Design and Implementation, Association for Computing
Machinery, 2021, pp. 1171–86, doi:10.1145/3453483.3454102.
short: J. Wang, Y. Sun, H. Fu, K. Chatterjee, A.K. Goharshady, in:, Proceedings
of the 42nd ACM SIGPLAN International Conference on Programming Language Design
and Implementation, Association for Computing Machinery, 2021, pp. 1171–1186.
conference:
end_date: 2021-06-26
location: Online
name: 'PLDI: Programming Language Design and Implementation'
start_date: 2021-06-20
date_created: 2021-07-11T22:01:18Z
date_published: 2021-06-01T00:00:00Z
date_updated: 2023-08-10T14:14:08Z
day: '01'
department:
- _id: KrCh
doi: 10.1145/3453483.3454102
ec_funded: 1
external_id:
arxiv:
- '2011.14617'
isi:
- '000723661700076'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2011.14617
month: '06'
oa: 1
oa_version: Preprint
page: 1171-1186
project:
- _id: 0599E47C-7A3F-11EA-A408-12923DDC885E
call_identifier: H2020
grant_number: '863818'
name: 'Formal Methods for Stochastic Models: Algorithms and Applications'
- _id: 267066CE-B435-11E9-9278-68D0E5697425
name: Quantitative Analysis of Probablistic Systems with a focus on Crypto-currencies
publication: Proceedings of the 42nd ACM SIGPLAN International Conference on Programming
Language Design and Implementation
publication_identifier:
isbn:
- '9781450383912'
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
scopus_import: '1'
status: public
title: Quantitative analysis of assertion violations in probabilistic programs
type: conference
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
year: '2021'
...
---
_id: '9645'
abstract:
- lang: eng
text: "We consider the fundamental problem of reachability analysis over imperative
programs with real variables. Previous works that tackle reachability are either
unable to handle programs consisting of general loops (e.g. symbolic execution),
or lack completeness guarantees (e.g. abstract interpretation), or are not automated
(e.g. incorrectness logic). In contrast, we propose a novel approach for reachability
analysis that can handle general and complex loops, is complete, and can be entirely
automated for a wide family of programs. Through the notion of Inductive Reachability
Witnesses (IRWs), our approach extends ideas from both invariant generation and
termination to reachability analysis.\r\n\r\nWe first show that our IRW-based
approach is sound and complete for reachability analysis of imperative programs.
Then, we focus on linear and polynomial programs and develop automated methods
for synthesizing linear and polynomial IRWs. In the linear case, we follow the
well-known approaches using Farkas' Lemma. Our main contribution is in the polynomial
case, where we present a push-button semi-complete algorithm. We achieve this
using a novel combination of classical theorems in real algebraic geometry, such
as Putinar's Positivstellensatz and Hilbert's Strong Nullstellensatz. Finally,
our experimental results show we can prove complex reachability objectives over
various benchmarks that were beyond the reach of previous methods."
acknowledgement: This research was partially supported by the ERC CoG 863818 (ForM-SMArt),
the National Natural Science Foundation of China (NSFC) Grant No. 61802254, the
Huawei Innovation Research Program, the Facebook PhD Fellowship Program, and DOC
Fellowship No. 24956 of the Austrian Academy of Sciences (ÖAW).
article_processing_charge: No
author:
- first_name: Ali
full_name: Asadi, Ali
last_name: Asadi
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Hongfei
full_name: Fu, Hongfei
id: 3AAD03D6-F248-11E8-B48F-1D18A9856A87
last_name: Fu
- first_name: Amir Kafshdar
full_name: Goharshady, Amir Kafshdar
id: 391365CE-F248-11E8-B48F-1D18A9856A87
last_name: Goharshady
orcid: 0000-0003-1702-6584
- first_name: Mohammad
full_name: Mahdavi, Mohammad
last_name: Mahdavi
citation:
ama: 'Asadi A, Chatterjee K, Fu H, Goharshady AK, Mahdavi M. Polynomial reachability
witnesses via Stellensätze. In: Proceedings of the 42nd ACM SIGPLAN International
Conference on Programming Language Design and Implementation. Association
for Computing Machinery; 2021:772-787. doi:10.1145/3453483.3454076'
apa: 'Asadi, A., Chatterjee, K., Fu, H., Goharshady, A. K., & Mahdavi, M. (2021).
Polynomial reachability witnesses via Stellensätze. In Proceedings of the 42nd
ACM SIGPLAN International Conference on Programming Language Design and Implementation
(pp. 772–787). Online: Association for Computing Machinery. https://doi.org/10.1145/3453483.3454076'
chicago: Asadi, Ali, Krishnendu Chatterjee, Hongfei Fu, Amir Kafshdar Goharshady,
and Mohammad Mahdavi. “Polynomial Reachability Witnesses via Stellensätze.” In
Proceedings of the 42nd ACM SIGPLAN International Conference on Programming
Language Design and Implementation, 772–87. Association for Computing Machinery,
2021. https://doi.org/10.1145/3453483.3454076.
ieee: A. Asadi, K. Chatterjee, H. Fu, A. K. Goharshady, and M. Mahdavi, “Polynomial
reachability witnesses via Stellensätze,” in Proceedings of the 42nd ACM SIGPLAN
International Conference on Programming Language Design and Implementation,
Online, 2021, pp. 772–787.
ista: 'Asadi A, Chatterjee K, Fu H, Goharshady AK, Mahdavi M. 2021. Polynomial reachability
witnesses via Stellensätze. Proceedings of the 42nd ACM SIGPLAN International
Conference on Programming Language Design and Implementation. PLDI: Programming
Language Design and Implementation, 772–787.'
mla: Asadi, Ali, et al. “Polynomial Reachability Witnesses via Stellensätze.” Proceedings
of the 42nd ACM SIGPLAN International Conference on Programming Language Design
and Implementation, Association for Computing Machinery, 2021, pp. 772–87,
doi:10.1145/3453483.3454076.
short: A. Asadi, K. Chatterjee, H. Fu, A.K. Goharshady, M. Mahdavi, in:, Proceedings
of the 42nd ACM SIGPLAN International Conference on Programming Language Design
and Implementation, Association for Computing Machinery, 2021, pp. 772–787.
conference:
end_date: 2021-06-26
location: Online
name: ' PLDI: Programming Language Design and Implementation'
start_date: 2021-06-20
date_created: 2021-07-11T22:01:17Z
date_published: 2021-06-01T00:00:00Z
date_updated: 2023-08-10T14:13:39Z
day: '01'
department:
- _id: KrCh
doi: 10.1145/3453483.3454076
ec_funded: 1
external_id:
isi:
- '000723661700050'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://hal.archives-ouvertes.fr/hal-03183862/
month: '06'
oa: 1
oa_version: Submitted Version
page: 772-787
project:
- _id: 0599E47C-7A3F-11EA-A408-12923DDC885E
call_identifier: H2020
grant_number: '863818'
name: 'Formal Methods for Stochastic Models: Algorithms and Applications'
- _id: 267066CE-B435-11E9-9278-68D0E5697425
name: Quantitative Analysis of Probablistic Systems with a focus on Crypto-currencies
publication: Proceedings of the 42nd ACM SIGPLAN International Conference on Programming
Language Design and Implementation
publication_identifier:
isbn:
- '9781450383912'
publication_status: published
publisher: Association for Computing Machinery
quality_controlled: '1'
scopus_import: '1'
status: public
title: Polynomial reachability witnesses via Stellensätze
type: conference
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
year: '2021'
...
---
_id: '10002'
abstract:
- lang: eng
text: 'We present a faster symbolic algorithm for the following central problem
in probabilistic verification: Compute the maximal end-component (MEC) decomposition
of Markov decision processes (MDPs). This problem generalizes the SCC decomposition
problem of graphs and closed recurrent sets of Markov chains. The model of symbolic
algorithms is widely used in formal verification and model-checking, where access
to the input model is restricted to only symbolic operations (e.g., basic set
operations and computation of one-step neighborhood). For an input MDP with n vertices
and m edges, the classical symbolic algorithm from the 1990s for the MEC decomposition
requires O(n2) symbolic operations and O(1) symbolic space. The only other
symbolic algorithm for the MEC decomposition requires O(nm−−√) symbolic operations
and O(m−−√) symbolic space. A main open question is whether the worst-case O(n2) bound
for symbolic operations can be beaten. We present a symbolic algorithm that requires O˜(n1.5) symbolic
operations and O˜(n−−√) symbolic space. Moreover, the parametrization of our
algorithm provides a trade-off between symbolic operations and symbolic space:
for all 0<ϵ≤1/2 the symbolic algorithm requires O˜(n2−ϵ) symbolic operations
and O˜(nϵ) symbolic space ( O˜ hides poly-logarithmic factors). Using our techniques
we present faster algorithms for computing the almost-sure winning regions of ω
-regular objectives for MDPs. We consider the canonical parity objectives for ω
-regular objectives, and for parity objectives with d -priorities we present
an algorithm that computes the almost-sure winning region with O˜(n2−ϵ) symbolic
operations and O˜(nϵ) symbolic space, for all 0<ϵ≤1/2 .'
acknowledgement: The authors are grateful to the anonymous referees for their valuable
comments. A. S. is fully supported by the Vienna Science and Technology Fund (WWTF)
through project ICT15–003. K. C. is supported by the Austrian Science Fund (FWF)
NFN Grant No S11407-N23 (RiSE/SHiNE) and by the ERC CoG 863818 (ForM-SMArt). For
M. H. the research leading to these results has received funding from the European
Research Council under the European Unions Seventh Framework Programme (FP/2007–2013)
/ ERC Grant Agreement no. 340506.
article_processing_charge: No
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Wolfgang
full_name: Dvorak, Wolfgang
last_name: Dvorak
- first_name: Monika H
full_name: Henzinger, Monika H
id: 540c9bbd-f2de-11ec-812d-d04a5be85630
last_name: Henzinger
orcid: 0000-0002-5008-6530
- first_name: Alexander
full_name: Svozil, Alexander
last_name: Svozil
citation:
ama: 'Chatterjee K, Dvorak W, Henzinger MH, Svozil A. Symbolic time and space tradeoffs
for probabilistic verification. In: Proceedings of the 36th Annual ACM/IEEE
Symposium on Logic in Computer Science. Institute of Electrical and Electronics
Engineers; 2021:1-13. doi:10.1109/LICS52264.2021.9470739'
apa: 'Chatterjee, K., Dvorak, W., Henzinger, M. H., & Svozil, A. (2021). Symbolic
time and space tradeoffs for probabilistic verification. In Proceedings of
the 36th Annual ACM/IEEE Symposium on Logic in Computer Science (pp. 1–13).
Rome, Italy: Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/LICS52264.2021.9470739'
chicago: Chatterjee, Krishnendu, Wolfgang Dvorak, Monika H Henzinger, and Alexander
Svozil. “Symbolic Time and Space Tradeoffs for Probabilistic Verification.” In
Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science,
1–13. Institute of Electrical and Electronics Engineers, 2021. https://doi.org/10.1109/LICS52264.2021.9470739.
ieee: K. Chatterjee, W. Dvorak, M. H. Henzinger, and A. Svozil, “Symbolic time and
space tradeoffs for probabilistic verification,” in Proceedings of the 36th
Annual ACM/IEEE Symposium on Logic in Computer Science, Rome, Italy, 2021,
pp. 1–13.
ista: 'Chatterjee K, Dvorak W, Henzinger MH, Svozil A. 2021. Symbolic time and space
tradeoffs for probabilistic verification. Proceedings of the 36th Annual ACM/IEEE
Symposium on Logic in Computer Science. LICS: Symposium on Logic in Computer Science,
1–13.'
mla: Chatterjee, Krishnendu, et al. “Symbolic Time and Space Tradeoffs for Probabilistic
Verification.” Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in
Computer Science, Institute of Electrical and Electronics Engineers, 2021,
pp. 1–13, doi:10.1109/LICS52264.2021.9470739.
short: K. Chatterjee, W. Dvorak, M.H. Henzinger, A. Svozil, in:, Proceedings of
the 36th Annual ACM/IEEE Symposium on Logic in Computer Science, Institute of
Electrical and Electronics Engineers, 2021, pp. 1–13.
conference:
end_date: 2021-07-02
location: Rome, Italy
name: 'LICS: Symposium on Logic in Computer Science'
start_date: 2021-06-29
date_created: 2021-09-12T22:01:24Z
date_published: 2021-07-07T00:00:00Z
date_updated: 2023-08-14T06:51:33Z
day: '07'
department:
- _id: KrCh
doi: 10.1109/LICS52264.2021.9470739
ec_funded: 1
external_id:
arxiv:
- '2104.07466'
isi:
- '000947350400089'
isi: 1
keyword:
- Computer science
- Computational modeling
- Markov processes
- Probabilistic logic
- Formal verification
- Game Theory
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2104.07466
month: '07'
oa: 1
oa_version: Preprint
page: 1-13
project:
- _id: 25863FF4-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S11407
name: Game Theory
- _id: 0599E47C-7A3F-11EA-A408-12923DDC885E
call_identifier: H2020
grant_number: '863818'
name: 'Formal Methods for Stochastic Models: Algorithms and Applications'
publication: Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer
Science
publication_identifier:
eisbn:
- 978-1-6654-4895-6
isbn:
- 978-1-6654-4896-3
issn:
- 1043-6871
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Symbolic time and space tradeoffs for probabilistic verification
type: conference
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
year: '2021'
...
---
_id: '10004'
abstract:
- lang: eng
text: 'Markov chains are the de facto finite-state model for stochastic dynamical
systems, and Markov decision processes (MDPs) extend Markov chains by incorporating
non-deterministic behaviors. Given an MDP and rewards on states, a classical optimization
criterion is the maximal expected total reward where the MDP stops after T steps,
which can be computed by a simple dynamic programming algorithm. We consider a
natural generalization of the problem where the stopping times can be chosen according
to a probability distribution, such that the expected stopping time is T, to optimize
the expected total reward. Quite surprisingly we establish inter-reducibility
of the expected stopping-time problem for Markov chains with the Positivity problem
(which is related to the well-known Skolem problem), for which establishing either
decidability or undecidability would be a major breakthrough. Given the hardness
of the exact problem, we consider the approximate version of the problem: we show
that it can be solved in exponential time for Markov chains and in exponential
space for MDPs.'
acknowledgement: We are grateful to the anonymous reviewers of LICS 2021 and of a
previous version of this paper for insightful comments that helped improving the
presentation. This research was partially supported by the grant ERC CoG 863818
(ForM-SMArt).
article_processing_charge: No
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Laurent
full_name: Doyen, Laurent
last_name: Doyen
citation:
ama: 'Chatterjee K, Doyen L. Stochastic processes with expected stopping time. In:
Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science.
Institute of Electrical and Electronics Engineers; 2021:1-13. doi:10.1109/LICS52264.2021.9470595'
apa: 'Chatterjee, K., & Doyen, L. (2021). Stochastic processes with expected
stopping time. In Proceedings of the 36th Annual ACM/IEEE Symposium on Logic
in Computer Science (pp. 1–13). Rome, Italy: Institute of Electrical and Electronics
Engineers. https://doi.org/10.1109/LICS52264.2021.9470595'
chicago: Chatterjee, Krishnendu, and Laurent Doyen. “Stochastic Processes with Expected
Stopping Time.” In Proceedings of the 36th Annual ACM/IEEE Symposium on Logic
in Computer Science, 1–13. Institute of Electrical and Electronics Engineers,
2021. https://doi.org/10.1109/LICS52264.2021.9470595.
ieee: K. Chatterjee and L. Doyen, “Stochastic processes with expected stopping time,”
in Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science,
Rome, Italy, 2021, pp. 1–13.
ista: 'Chatterjee K, Doyen L. 2021. Stochastic processes with expected stopping
time. Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science.
LICS: Symposium on Logic in Computer Science, 1–13.'
mla: Chatterjee, Krishnendu, and Laurent Doyen. “Stochastic Processes with Expected
Stopping Time.” Proceedings of the 36th Annual ACM/IEEE Symposium on Logic
in Computer Science, Institute of Electrical and Electronics Engineers, 2021,
pp. 1–13, doi:10.1109/LICS52264.2021.9470595.
short: K. Chatterjee, L. Doyen, in:, Proceedings of the 36th Annual ACM/IEEE Symposium
on Logic in Computer Science, Institute of Electrical and Electronics Engineers,
2021, pp. 1–13.
conference:
end_date: 2021-07-02
location: Rome, Italy
name: 'LICS: Symposium on Logic in Computer Science'
start_date: 2021-06-29
date_created: 2021-09-12T22:01:25Z
date_published: 2021-07-07T00:00:00Z
date_updated: 2023-08-14T06:52:07Z
day: '07'
department:
- _id: KrCh
doi: 10.1109/LICS52264.2021.9470595
ec_funded: 1
external_id:
arxiv:
- '2104.07278'
isi:
- '000947350400036'
isi: 1
keyword:
- Computer science
- Heuristic algorithms
- Memory management
- Automata
- Markov processes
- Probability distribution
- Complexity theory
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2104.07278
month: '07'
oa: 1
oa_version: Preprint
page: 1-13
project:
- _id: 0599E47C-7A3F-11EA-A408-12923DDC885E
call_identifier: H2020
grant_number: '863818'
name: 'Formal Methods for Stochastic Models: Algorithms and Applications'
publication: Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer
Science
publication_identifier:
eisbn:
- 978-1-6654-4895-6
isbn:
- 978-1-6654-4896-3
issn:
- 1043-6871
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Stochastic processes with expected stopping time
type: conference
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
year: '2021'
...
---
_id: '10055'
abstract:
- lang: eng
text: "Repeated idempotent elements are commonly used to characterise iterable behaviours
in abstract models of computation. Therefore, given a monoid M, it is natural
to ask how long a sequence of elements of M needs to be to ensure the presence
of consecutive idempotent factors. This question is formalised through the notion
of the Ramsey function R_M associated to M, obtained by mapping every k ∈ ℕ to
the minimal integer R_M(k) such that every word u ∈ M^* of length R_M(k) contains
k consecutive non-empty factors that correspond to the same idempotent element
of M. In this work, we study the behaviour of the Ramsey function R_M by investigating
the regular \U0001D49F-length of M, defined as the largest size L(M) of a submonoid
of M isomorphic to the set of natural numbers {1,2, …, L(M)} equipped with the
max operation. We show that the regular \U0001D49F-length of M determines the
degree of R_M, by proving that k^L(M) ≤ R_M(k) ≤ (k|M|⁴)^L(M). To allow applications
of this result, we provide the value of the regular \U0001D49F-length of diverse
monoids. In particular, we prove that the full monoid of n × n Boolean matrices,
which is used to express transition monoids of non-deterministic automata, has
a regular \U0001D49F-length of (n²+n+2)/2."
acknowledgement: This project has received funding from the European Union’s Horizon
2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement
No. 754411. I wish to thank Michaël Cadilhac, Emmanuel Filiot and Charles Paperman
for their valuable insights concerning Green’s relations.
alternative_title:
- LIPIcs
article_number: '44'
article_processing_charge: No
author:
- first_name: Ismael R
full_name: Jecker, Ismael R
id: 85D7C63E-7D5D-11E9-9C0F-98C4E5697425
last_name: Jecker
citation:
ama: 'Jecker IR. A Ramsey theorem for finite monoids. In: 38th International
Symposium on Theoretical Aspects of Computer Science. Vol 187. Schloss Dagstuhl
- Leibniz Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.STACS.2021.44'
apa: 'Jecker, I. R. (2021). A Ramsey theorem for finite monoids. In 38th International
Symposium on Theoretical Aspects of Computer Science (Vol. 187). Saarbrücken,
Germany: Schloss Dagstuhl - Leibniz Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.STACS.2021.44'
chicago: Jecker, Ismael R. “A Ramsey Theorem for Finite Monoids.” In 38th International
Symposium on Theoretical Aspects of Computer Science, Vol. 187. Schloss Dagstuhl
- Leibniz Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.STACS.2021.44.
ieee: I. R. Jecker, “A Ramsey theorem for finite monoids,” in 38th International
Symposium on Theoretical Aspects of Computer Science, Saarbrücken, Germany,
2021, vol. 187.
ista: 'Jecker IR. 2021. A Ramsey theorem for finite monoids. 38th International
Symposium on Theoretical Aspects of Computer Science. STACS: Symposium on Theoretical
Aspects of Computer Science, LIPIcs, vol. 187, 44.'
mla: Jecker, Ismael R. “A Ramsey Theorem for Finite Monoids.” 38th International
Symposium on Theoretical Aspects of Computer Science, vol. 187, 44, Schloss
Dagstuhl - Leibniz Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.STACS.2021.44.
short: I.R. Jecker, in:, 38th International Symposium on Theoretical Aspects of
Computer Science, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021.
conference:
end_date: 2021-03-19
location: Saarbrücken, Germany
name: 'STACS: Symposium on Theoretical Aspects of Computer Science'
start_date: 2021-03-16
date_created: 2021-09-27T14:33:15Z
date_published: 2021-03-10T00:00:00Z
date_updated: 2023-08-14T07:03:23Z
day: '10'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.4230/LIPIcs.STACS.2021.44
ec_funded: 1
external_id:
isi:
- '000635691700044'
file:
- access_level: open_access
checksum: 17432a05733f408de300e17e390a90e4
content_type: application/pdf
creator: cchlebak
date_created: 2021-10-01T09:55:00Z
date_updated: 2021-10-01T09:55:00Z
file_id: '10063'
file_name: 2021_LIPIcs_Jecker.pdf
file_size: 720250
relation: main_file
success: 1
file_date_updated: 2021-10-01T09:55:00Z
has_accepted_license: '1'
intvolume: ' 187'
isi: 1
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 38th International Symposium on Theoretical Aspects of Computer Science
publication_identifier:
isbn:
- 978-3-9597-7180-1
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: A Ramsey theorem for finite monoids
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 187
year: '2021'
...