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Highly Undecidable Questions for Process Algebras

Petr Jancar, Jirí Srba
2004 BRICS Report Series  
We also show Pi^1_1-hardness of weak omega-trace equivalence 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.  ... 
doi:10.7146/brics.v11i8.21833 fatcat:etmvtxf2gzbbtbcjddqxqa27um

Highly Undecidable Questions for Process Algebras [chapter]

Petr Jančar, Jiři Srba Brics
IFIP International Federation for Information Processing  
We also show of weak equivalence 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.  ... 
doi:10.1007/1-4020-8141-3_39 dblp:conf/ifipTCS/JancarS04 fatcat:hm7kvkfe6jcrjpjvu7w5dpuaye

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.  ... 

Analyses of the Responses of Staff and Students on Mathematics Mentoring in Isuikwuato Local Government Area, Abia State, Nigeria

Silas A. Ihedioha
2015 OALib  
Such important effort to the development of the students needs re-examined to assert successes 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.  ... 
doi:10.4236/oalib.1102035 fatcat:45g2cpsqhfbbnd4xuf2ivqgeua

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.  ... 

Standing on the Shoulders of a Giant [chapter]

David Harel
2012 Lecture Notes in Computer Science  
And we are left with the tantalizing 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] .  ... 
doi:10.1007/978-3-642-31585-5_3 fatcat:4id6bogevfdhdcvdljqjggaj4i

Standing on the shoulders of a giant

David Harel
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 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] .  ... 
doi:10.1145/2325296.2325300 dblp:conf/iticse/Harel12 fatcat:ewdxigkeinferhzxxprcrzgksi

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  ... 

Undecidability and incompleteness in classical mechanics

N. C. A. da Costa, F. A. Doria
1991 International Journal of Theoretical Physics  
We then derive a general 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  ... 
doi:10.1007/bf00671484 fatcat:n6nds2sg5banfmieriz63tzsgy

Formal Methods [chapter]

Olav Lysne
2018 The Huawei and Snowden Questions  
These appeared more or less at the same time and were developed in parallel 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  ... 
doi:10.1007/978-3-319-74950-1_9 fatcat:53ws4lrhg5ayho7owbk6r3jskq

Decidability Problems for Self-induced Systems Generated by a Substitution [chapter]

Timo Jolivet, Anne Siegel
2015 Lecture Notes in Computer Science  
They are somehow ubiquitous as self-replication 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.  ... 
doi:10.1007/978-3-319-23111-2_1 fatcat:el3vc7rc5natvlx6xjwqrgjit4

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]

Jochen Koenigsmann
2013 arXiv   pre-print
These lecture notes cover classical 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] ).  ... 
arXiv:1309.0441v1 fatcat:ndb52ta63rdilgojjewavp2wqi

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  ... 

Towards a Notion of Distributed Time for Petri Nets [chapter]

Mogens Nielsen, Vladimiro Sassone, Jiří Srba
2001 Lecture Notes in Computer Science  
We set the ground 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  ... 
doi:10.1007/3-540-45740-2_3 fatcat:e25csyz3rnbj5adrbpsaab5rou
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