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Modular term rewriting systems and the termination

Masahito Kurihara, Ikuo Kaji
1990 Information Processing Letters  
Acknowledgment The authors would like to thank Y. Toyama for discussing the definitions  ...  Then a modular term rewriting system MR on .7( F, V) is a family of term rewriting systems R, on 7( 3, V), i.e., MR = {R,, . . . , R, }. Each member R, is called a module of MR.  ...  Remarks on modularity In this section we make some remarks on modularity, by comparing from several viewpoints the modular TRSs with the union of TRSs.  ... 
doi:10.1016/0020-0190(90)90221-i fatcat:5po5kwbairc47dtvnnvxuu7464

PSPACE-completeness of Modular Supervisory Control Problems*

Kurt Rohloff, St�phane Lafortune
2005 Discrete event dynamic systems  
in the study of such Blarge-scale^systems.  ...  In this paper we investigate computational issues associated with the supervision of concurrent processes modeled as modular discrete-event systems.  ...  Proof: This proof is a modified version of the proof in (Kozen, 1977) that shows the DFA-Int problem is PSPACE-complete.  ... 
doi:10.1007/s10626-004-6210-5 fatcat:kogatmtijzc5nkcihy3upbgkr4

Partial solution to Mackey's problem about modular pairs and completeness

Samuel S. Holland
1969 Canadian Journal of Mathematics - Journal Canadien de Mathematiques  
Dual-modular pairs of subspaces.  ...  that the elements of J^ that satisfy M = M (elements we shall call closed) constitute a complete latticed under the same order as that in Jf, where now the meet operation ( A ) in =£f is the same as that  ...  Therefore M' + N' is regularly closed, (M' f N') is a dual-modular pair, thus (M, N) is a modular pair. That completes the proof of Theorem 6.  ... 
doi:10.4153/cjm-1969-166-3 fatcat:uolmuhjxezcl7mhyfmgwyjr4me

Modular extensions of point-modular lattices

R. J. Mihalek
1966 Proceedings of the Japan Academy  
Then a point-modular point-complemented lattice L is decomposed into a subdirect union of point-modular point-complemented irreducible lattices and in the case that L is complete into the direct union.  ...  Mackey 5 for which he states conditions that a family of subspaces of a (real) linear space be the family of closed subspaces relative to some regular linear system constructed on the linear space.  ...  The system (L, /, .) is a point-modular pointcomplemented lattice. Proof. It is immediate that the system is a lattice. For the point-modularity let b, c, p e L with O-4p<___c.  ... 
doi:10.3792/pja/1195522080 fatcat:w5xil3dzx5e5bpsbn7tjlk4wjq

Modular proofs for completeness of hierarchical term rewriting systems

M.R.K.Krishna Rao
1995 Theoretical Computer Science  
We propose a set of sufficient conditions for the modularity of completeness of hierarchical combinations.  ...  Then the modularity of completeness is obtained using a recent result relating strong innermost normalization and termination properties of locally confluent overlay systems.  ...  The author is grateful to the referees for many suggestions in improving the presentation very much.  ... 
doi:10.1016/0304-3975(95)00075-8 fatcat:hp5rkbjavnab3fj6fq3fuohbvu

Page 3376 of Mathematical Reviews Vol. , Issue 91F [page]

1991 Mathematical Reviews  
It is shown in the monograph under review that the combination of composi- tional completeness together with adaptation completeness implies modular completeness of a proof system.  ...  In addition to compositional completeness, new no- tions of so-called modular completeness and adaptational com- pleteness of proof systems are introduced.  ... 

Complexity of Detectability, Opacity and A-Diagnosability for Modular Discrete Event Systems [article]

Tomáš Masopust, Xiang Yin
2017 arXiv   pre-print
We study the complexity of deciding whether a modular discrete event system is detectable (resp. opaque, A-diagnosable).  ...  Consequently, if the systems are all fully observable, then deciding weak detectability (opacity) for modular systems is PSPACE-complete.  ...  Acknowledgements The research of T. Masopust was supported by the GAČR project GA15-02532S and by RVO 67985840.  ... 
arXiv:1710.02877v1 fatcat:a6wdyfwntng3bc54hxetfiyqem

Connectedness of Hecke Algebras and the Rayuela conjecture: a path to functoriality and modularity [article]

Luis Dieulefait, Ariel Pacetti
2014 arXiv   pre-print
We prove a weak version of the modular variant using the connectedness of certain Hecke algebras, and we comment on possible applications of these results to establish some cases of Langlands functoriality  ...  Such conjecture implies the generalized Serre's conjecture and is equivalent to Serre's conjecture under a modular version of it.  ...  In particular, the system {ρ 2,λ } is also modular. Proof. The procedure is quite similar to the one in the previous Theorem, but now we can use Theorem 3.1.  ... 
arXiv:1402.6270v2 fatcat:rfywfwffzfgcfi3eik3oo33ity

Model Complete Expansions of the Real Field by Modular Functions and Forms [article]

Ricardo Bianconi
2014 arXiv   pre-print
This is done using ideas of Peterzil and Starchenko's paper peterzil-starchenko-wp2004 on the uniform definability of function in R_an (and of the modular function J).  ...  We prove a strong form of model completenes for expansions of the field of real numbers by (the real and imaginary parts of) the modular function J, by the modular forms E_4 and E_6 and quasimodular form  ...  A question directly related with this work is wether the (full) exponential function is necessary to prove the model completeness of those structures.  ... 
arXiv:1406.7158v1 fatcat:z5lmgb3nwrdxvcifmodawmdphy

Covariants of Binary Modular Groups

O. E. Glenn
1919 Proceedings of the National Academy of Sciences of the United States of America  
A complete system of the quadratic, modulo 3.  ...  -I have proved that the following eighteen quantics constitute a complete formal system modulo 3 of f2; the proof resting primarily upon the fact that, when p = 3, every covariant is of even order, and  ... 
doi:10.1073/pnas.5.4.107 pmid:16576354 pmcid:PMC1091545 fatcat:t4g6u7zmmvaejd7zk5v7wloxsq

Unravelings and ultra-properties [chapter]

Massimo Marchiori
1996 Lecture Notes in Computer Science  
We show how to rediscover properties like decreasingness, and to give easy proofs of some existing results on CTRSs.  ...  Moreover, we show how unravelings provide a valuable tool to study modularity of CTRSs, automatically giving a multitude of new results.  ...  Lemma 5.1 Uis complete for the following properties: being non-collapsing, non-overlapping, constructor system, overlay system.  ... 
doi:10.1007/3-540-61735-3_7 fatcat:rgmk4g7zsjcbvluxrz2smul5py

Page 6989 of Mathematical Reviews Vol. , Issue 96k [page]

1996 Mathematical Reviews  
As an easy con- sequence this latter result also entails a simplified proof of the fact that completeness is a decomposable property of constructor systems.  ...  Summary: “We present a collection of results on regular tree lan- guages and rewrite systems. Moreover we prove the undecidability of the preservation of regularity by rewrite systems.  ... 

Semi-completeness of hierarchical and super-hierarchical combinations of term rewriting systems [chapter]

M. R. K. Krishna Rao
1995 Lecture Notes in Computer Science  
In this paper, we study modular aspects of hierarchical and super hierarchical combinations of term rewriting systems.  ...  We first establish modularity of weak normalization for this class (defined by the sufficient condition) and modularity of semi-completeness for a class of crosswise independent unions.  ...  The modularity of semi-completeness follows from the above theorem and Staples' lemma. Then, the combined system 760 U 761 i8 semi-complete as well.  ... 
doi:10.1007/3-540-59293-8_208 fatcat:algbduxhqzdfxay7bdxnyzsfs4

Modular Properties of Composable Term Rewriting Systems

Enno Ohlebusch
1995 Journal of symbolic computation  
Most of the known modularity results for the former systems hold for disjoint or constructor-sharing combinations. Here we focus on a more general kind of combination: so-called composable systems.  ...  As far as conditional term rewriting systems are concerned, all known modularity result but one apply only to disjoint systems. Here we investigate conditional systems which may share constructors.  ...  Acknowledgements I am grateful to Aart Middeldorp and the referees for their comments on the paper.  ... 
doi:10.1006/jsco.1995.1036 fatcat:igpsgira6nbl7kbe3dq3euaovi

Explicit non-normal modal logic [article]

Atefeh Rohani, Thomas Studer
2022 arXiv   pre-print
We establish soundness and completeness with respect to various models and we study the problem of realization.  ...  Faroldi argues that deontic modals are hyperintensional and thus traditional modal logic cannot provide an appropriate formalization of deontic situations.  ...  Proof. As usual, the proof is by induction on the length of JE CS derivations and a case distinction on the last rule. The only interesting case is when F is an instance of je.  ... 
arXiv:2108.04486v2 fatcat:segoxd6rtned7mxioufjgrn43a
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