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Highly Undecidable Questions for Process Algebras

2004
*
BRICS Report Series
*

We also show Pi^1_1-hardness of weak omega-trace equivalence

doi:10.7146/brics.v11i8.21833
fatcat:etmvtxf2gzbbtbcjddqxqa27um
*for*the (sub)classes BPA (basic*process**algebra*) and BPP (basic parallel*processes*). ... We show Sigma^1_1-completeness of weak bisimilarity*for*PA (*process**algebra*), and of weak simulation preorder/equivalence*for*PDA (pushdown automata), PA and PN (Petri nets). ... Of particular interest is the*question*whether some other equivalences are also*highly**undecidable*(i.e., beyond (hyper)arithmetical hierarchy). We provide a few results and notes about this. ...##
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Highly Undecidable Questions for Process Algebras
[chapter]

*
IFIP International Federation for Information Processing
*

We also show of weak equivalence

doi:10.1007/1-4020-8141-3_39
dblp:conf/ifipTCS/JancarS04
fatcat:hm7kvkfe6jcrjpjvu7w5dpuaye
*for*the (sub)classes BPA (basic*process**algebra*) and BPP (basic parallel*processes*). ... We show of weak bisimilarity*for*PA (*process**algebra*), and of weak simulation preorder/equivalence*for*PDA (pushdown automata), PA and PN (Petri nets). ... PPDA) system is called BPA*for*basic*process**algebra*(resp. BPP*for*basic parallel*processes*) whenever the set of control states is singleton. ...##
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Page 4087 of Mathematical Reviews Vol. , Issue 2004e
[page]

2004
*
Mathematical Reviews
*

Summary: “Section | presents the main

*questions*associated with the application of the*algebraic*approach to pattern recognition and classification. ... However, the problem is also*undecidable**for*total reward or average reward criteria. ...##
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Analyses of the Responses of Staff and Students on Mathematics Mentoring in Isuikwuato Local Government Area, Abia State, Nigeria

2015
*
OALib
*

Such important effort to the development of the students needs re-examined to assert successes

doi:10.4236/oalib.1102035
fatcat:45g2cpsqhfbbnd4xuf2ivqgeua
*for*its continuation or failures*for*the reorganization of its implementation, hence this study. ... They were asked to indicate their opinion on how the mentoring exercise has imparted on the students' performance in*Algebra*. ... The female teachers rate 33.3% 16.7% and 50%*for*No,*undecided*and Yes, respectively, while the female students results are 16.89%, 16.89% and 66.22%*for*No,*undecided*and Yes, respectively. ...##
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Page 4542 of Mathematical Reviews Vol. , Issue 93h
[page]

1993
*
Mathematical Reviews
*

The above generalization makes it possible to prove that the semiunification problem

*for*finite feature*algebras*is*undecidable*. ...*Process*. Lett. 44 (1992), no. 6, 297-302. ...##
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Standing on the Shoulders of a Giant
[chapter]

2012
*
Lecture Notes in Computer Science
*

And we are left with the tantalizing

doi:10.1007/978-3-642-31585-5_3
fatcat:4id6bogevfdhdcvdljqjggaj4i
*question*of what would he have achieved had he lived another 30 or 40 years. ... He carried out pioneering work on the idea of mathematical and computational modeling of biology, but also dealt with the*question*whether computers can be of human-like intelligence. ... Finally, I was able to show that asking whether a recursive graph has a Hamiltonian path is also*highly**undecidable*, i.e., complete*for*the Σ 1 1 /Π 1 1 level [12] . ...##
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Standing on the shoulders of a giant

2012
*
Proceedings of the 17th ACM annual conference on Innovation and technology in computer science education - ITiCSE '12
*

And we are left with the tantalizing

doi:10.1145/2325296.2325300
dblp:conf/iticse/Harel12
fatcat:ewdxigkeinferhzxxprcrzgksi
*question*of what would he have achieved had he lived another 30 or 40 years. ... He carried out pioneering work on the idea of mathematical and computational modeling of biology, but also dealt with the*question*whether computers can be of human-like intelligence. ... Finally, I was able to show that asking whether a recursive graph has a Hamiltonian path is also*highly**undecidable*, i.e., complete*for*the Σ 1 1 /Π 1 1 level [12] . ...##
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Page 3218 of Mathematical Reviews Vol. , Issue 86g
[page]

1986
*
Mathematical Reviews
*

Author summary: “We show that the validity problem

*for*propo- sitional dynamic logic (PDL), which is decidable and actually DEXPTIME-complete*for*the usual class of regular programs, becomes*highly**undecidable*... We intend only to characterize all possible*processes*in a given event domain and to leave the*question*of properties of their sets to more specific theories of concurrent systems (similar to the theory ...##
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Undecidability and incompleteness in classical mechanics

1991
*
International Journal of Theoretical Physics
*

We then derive a general

doi:10.1007/bf00671484
fatcat:n6nds2sg5banfmieriz63tzsgy
*undecidability*and incompleteness result*for*elementary functions within ZFC set theory, and apply it to some problems in Hamiltonian mechanics and dynamical systems theory. ... A similar application to the unsolvability of the decision problem*for*chaotic dynamical systems is also obtained. ... ACKNOWLEDGMENTS The*questions*discussed in the present paper arose out of a series of seminars given by F.A.D. at the University of S~o Paulo's Institute*for*Advanced Studies at the invitation of the first ...##
###
Formal Methods
[chapter]

2018
*
The Huawei and Snowden Questions
*

These appeared more or less at the same time and were developed in parallel

doi:10.1007/978-3-319-74950-1_9
fatcat:53ws4lrhg5ayho7owbk6r3jskq
*for*a long time. Later, several variants of*process**algebras*were introduced. ... This led to the development of*process**algebras*, which, in the context of specification, have the commonalities that they describe the*processes*of a parallel program and that these*processes*communicate ...##
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Decidability Problems for Self-induced Systems Generated by a Substitution
[chapter]

2015
*
Lecture Notes in Computer Science
*

They are somehow ubiquitous as self-replication

doi:10.1007/978-3-319-23111-2_1
fatcat:el3vc7rc5natvlx6xjwqrgjit4
*processes*appear naturally in several fields of mathematics. ... We will end up this talk by discussing new*questions*arising in relation with continued fraction algorithm and fractal tiles generated by S-adic expansion systems. ... repetitive*processes*or replacement rules occur. ...##
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Page 2837 of Mathematical Reviews Vol. , Issue 89E
[page]

1989
*
Mathematical Reviews
*

Up to now this problem, known to be

*highly**undecidable*, has been solved*for*relatively few types of languages: the usual proofs involve combinatorial arguments and consider all possible grammars*for*the ... Some*undecidability*re- sults are also presented. I. M. ...##
###
Undecidability in number theory
[article]

2013
*
arXiv
*
pre-print

These lecture notes cover classical

arXiv:1309.0441v1
fatcat:ndb52ta63rdilgojjewavp2wqi
*undecidability*results in number theory, Hilbert's 10th problem and recent developments around it, also*for*rings other than the integers. ...*for*their immense interest, their encouraging*questions*and their critical remarks. ... A positive answer to an analogue of this*question*is Lipshitz's result that addition and divisibility over Z is ∃-decidable, but ∀∃-*undecidable*( [Lip78] ). ...##
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Page 4694 of Mathematical Reviews Vol. , Issue 81K
[page]

1981
*
Mathematical Reviews
*

N. 81k:68004
On the

*question*of the use, in*highly*exact modular calculations on a computer, of bases of a special type. ... Reichel, Initially-restricting*algebraic*theories (pp. 504-514); Wolfgang Re- isig, Schemes*for*nonsequential*processing*systems (pp. 515-527); Jan Reiterman and Véra Trnkova, Dynamic*algebras*which are ...##
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Towards a Notion of Distributed Time for Petri Nets
[chapter]

2001
*
Lecture Notes in Computer Science
*

We set the ground

doi:10.1007/3-540-45740-2_3
fatcat:e25csyz3rnbj5adrbpsaab5rou
*for*research on a timed extension of Petri nets where time parameters are associated with tokens and arcs carry constraints that qualify the age of tokens required*for*enabling. ... We give a formal definition of the model and investigate properties of local versus global timing, including decidability issues and notions of*processes*of the respective models. ... Recently algorithmic methods have been developed*for**process**algebras*generating infinite state systems [Mol96, BE97] , timed*process**algebra*[Yi90] , Petri nets [Jan90] , lossy vector addition systems ...
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