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A hierarchy of proof rules for checking positive invariance of algebraic and semi-algebraic sets

Khalil Ghorbal, Andrew Sogokon, André Platzer
2017 Computer languages, systems & structures  
This paper studies sound proof rules for checking positive invariance of algebraic and semi-algebraic sets, that is, sets satisfying polynomial equalities and those satisfying finite boolean combinations  ...  We study the trade-off between proof rule generality and practical performance and evaluate our theoretical observations on a set of benchmarks.  ...  Jackson at the LFCS, University of Edinburgh, for his valuable help in improving the manuscript.  ... 
doi:10.1016/j.cl.2015.11.003 fatcat:f3ujzbyofvfsfguwhtg6g7vhwm

A Hierarchy of Proof Rules for Checking Differential Invariance of Algebraic Sets [chapter]

Khalil Ghorbal, Andrew Sogokon, André Platzer
2015 Lecture Notes in Computer Science  
This paper presents a theoretical and experimental comparison of sound proof rules for proving invariance of algebraic sets, that is, sets satisfying polynomial equalities, under the flow of polynomial  ...  We study the trade-off between proof rule generality and practical performance and evaluate our theoretical observations on a set of heterogeneous benchmarks.  ...  Jackson at the LFCS, University of Edinburgh, for his valuable help in improving the manuscript.  ... 
doi:10.1007/978-3-662-46081-8_24 fatcat:wa3q2u5n3bdarj7cazaiksyo6a

Predicate Transformer Semantics for Hybrid Systems: Verification Components for Isabelle/HOL [article]

Jonathan Julián Huerta y Munive, Georg Struth
2021 arXiv   pre-print
It supports reasoning about the temporal evolutions of hybrid programs in the style of differential dynamic logic modelled by flows or invariant sets for vector fields.  ...  We present a semantic framework for the deductive verification of hybrid systems with Isabelle/HOL.  ...  We would also like to thank our referees for pointers to related work and many suggestions that helped us to improve the presentation of this work and reflect on its contributions.  ... 
arXiv:1909.05618v3 fatcat:7lnrnamltvcutgxfezop4akt7q

Polynomial hierarchy, Betti numbers and a real analogue of Toda's theorem [article]

Saugata Basu, Thierry Zell
2010 arXiv   pre-print
sentences in the first order theory of the reals with a constant number of quantifier alternations, and that of computing Betti numbers of semi-algebraic sets.  ...  In this paper we formulate and prove a real analogue of Toda's theorem.  ...  If one thinks of "counting" a semi-algebraic set S ⊂ R k as computing a certain discrete invariant, then a natural well-studied discrete topological invariant of S is its Euler-Poincaré characteristic.  ... 
arXiv:0812.1200v3 fatcat:yrzbjmklv5akrhnhaajigg4nmi

Polynomial Hierarchy, Betti Numbers and a Real Analogue of Toda's Theorem

Saugata Basu, Thierry Zell
2009 2009 50th Annual IEEE Symposium on Foundations of Computer Science  
in the first order theory of the reals with a constant number of quantifier alternations, and that of computing Betti numbers of semialgebraic sets.  ...  This latter result might be of independent interest to researchers in algorithmic semi-algebraic geometry.  ...  If one thinks of "counting" a semi-algebraic set S ⊂ R k as computing a certain discrete invariant, then a natural well-studied discrete topological invariant of S is its Euler-Poincaré characteristic.  ... 
doi:10.1109/focs.2009.70 dblp:conf/focs/BasuZ09 fatcat:fqcolbqwqvf5pd7pcjsbrhk2li

From differential crossed modules to tensor hierarchies [article]

Sylvain Lavau, Jim Stasheff
2021 arXiv   pre-print
Gauging procedures in supergravity rely on a pairing -- the embedding tensor -- between a Leibniz algebra and a Lie algebra.  ...  We deem the present construction of such tensor hierarchies clearer and more straightforward than previous derivations.  ...  He is also grateful to Georges Skandalis and Stéphane Vassout, for having funded most  ... 
arXiv:2003.07838v3 fatcat:f4eb72gj6rfmfot35vargpdmxq

Incorporating XSL Processing Into Database Engines [chapter]

Guido Moerkotte
2002 VLDB '02: Proceedings of the 28th International Conference on Very Large Databases  
Further, we present algorithms to optimize the template rule selection process and the algebraic expression resulting from the translation.  ...  The two observations that 1) many XML documents are stored in a database or generated from data stored in a database and 2) processing these documents with XSL stylesheet processors is an important, often  ...  I thank Simone Seeger for her help in preparing the manuscript and Thorsten Fiebig for many fruitful discussions.  ... 
doi:10.1016/b978-155860869-6/50018-4 dblp:conf/vldb/Moerkotte02 fatcat:3yizxwprqje33kuctqqrnrzove

A landscape of contact manifolds via rational SFT [article]

Agustin Moreno, Zhengyi Zhou
2021 arXiv   pre-print
The hierarchy functor consists of three levels of structures, namely algebraic planar torsion, order of semi-dilation and planarity, all taking values in ℕ∪{∞}, where algebraic planar torsion can be understood  ...  We define a hierarchy functor from the exact symplectic cobordism category to a totally ordered set from a BL_∞ (Bi-Lie) formalism of the rational symplectic field theory (RSFT).  ...  Semi-dilations In this section, we introduce an inner hierarchy called the order of semi-dilation for the P = 1 case.  ... 
arXiv:2012.04182v2 fatcat:t6d4oorh7bhvlnapqndth5mhnm

On the Kadomtsev-Petviashvili hierarchy in an extended class of formal pseudo-differential operators [article]

Jean-Pierre Magnot, Vladimir Rubtsov
2021 arXiv   pre-print
The classical algebra Ψ DO(S^1,^n) where the KP hierarchy is well-known appears as a subalgebra of Cl(S^1,^n).  ...  We study the existence and uniqueness of the Kadomtsev-Petviashvili (KP) hierarchy solutions in the algebra of Cl(S^1,^n) of formal classical pseudo-differential operators.  ...  Classical algebraic settings that arise in the theory of the KP hierarchy will be reviewed in section 1.3, in section 1.4 and in section 1.7.  ... 
arXiv:2101.04523v1 fatcat:4s3v4mw54nh2digztrjvxgfxyu

A convergent inflation hierarchy for quantum causal structures [article]

Laurens T. Ligthart, Mariami Gachechiladze, David Gross
2021 arXiv   pre-print
A main technical ingredient to our proof is a Quantum de Finetti Theorem that holds for general tensor products of C^*-algebras, generalizing previous work that was restricted to minimal tensor products  ...  An inflation hierarchy has also been formulated for causal structures that allow for the observed classical random variables to arise from measurements on quantum states - however, no proof of completeness  ...  This work has been supported by Germany's Excellence Strategy -Cluster of Excellence Matter and Light for Quantum Computing (ML4Q) EXC 2004/1 -390534769.  ... 
arXiv:2110.14659v2 fatcat:5jy55ws2lvaa5gflvt7ebgnwku

Unifying Known Lower Bounds via Geometric Complexity Theory

Joshua A. Grochow
2014 2014 IEEE 29th Conference on Computational Complexity (CCC)  
That is, the original proofs, with what is often just a little extra work, already provide representation-theoretic obstructions in the sense of GCT for their respective lower bounds.  ...  This enables us to expose a new viewpoint on GCT, whereby it is a natural unification of known results and broad generalization of known techniques.  ...  Landsberg, Ketan Mulmuley, Toni Pitassi, Peter Scheiblechner, Chris Umans, Alasdair Urquhart, Ryan Williams, and Yiwei She for useful discussions. In particular, Williams suggested the  ... 
doi:10.1109/ccc.2014.35 dblp:conf/coco/Grochow14 fatcat:z5eytgp64jh2pclri4tlmky53e

Finite and Infinite W Algebras and their Applications [article]

T.Tjin
1993 arXiv   pre-print
The problem of quantising the DS reductions is solved for arbitrary sl_2 embeddings and it is shown that any W algebra can be embedded into an affine Lie algebra.  ...  In this paper we present a systematic study of W algebras from the Hamiltonian reduction point of view.  ...  The action S[g] is conformally invariant for k positive and In fact the action (5.2.21) is only called the WZW action for this value of λ.  ... 
arXiv:hep-th/9308146v1 fatcat:linuwadq5bb5rnr5b2cfkewf3m

Unifying Known Lower Bounds via Geometric Complexity Theory

Joshua A. Grochow
2015 Computational Complexity  
That is, the original proofs, with what is often just a little extra work, already provide representation-theoretic obstructions in the sense of GCT for their respective lower bounds.  ...  This enables us to expose a new viewpoint on GCT, whereby it is a natural unification and broad generalization of known results.  ...  Landsberg, Ketan Mulmuley, Toni Pitassi, Peter Scheiblechner, Chris Umans, Alasdair Urquhart, Ryan Williams, and Yiwei She for useful discussions. In particular, Williams suggested the  ... 
doi:10.1007/s00037-015-0103-x fatcat:ifoaveduubhmxlokr4pygqzjqq

Regular conjugacy classes in the Weyl group and integrable hierarchies

F Delduc, L Feher
1995 Journal of Physics A: Mathematical and General  
Generalized KdV hierarchies associated by Drinfeld-Sokolov reduction to grade one regular semisimple elements from non-equivalent Heisenberg subalgebras of a loop algebra ⊗ C[λ,λ^-1] are studied.  ...  For a classical Lie algebra, we derive pseudo-differential Lax operators for those non-principal KdV systems that can be obtained as discrete reductions of KdV systems related to gl_n.  ...  Toppan and J. Underwood for discussions. We are grateful to I.R. McIntosh for making available ref. [11] and to a referee for drawing our attention to ref. [27] . We are indebted to A.  ... 
doi:10.1088/0305-4470/28/20/016 fatcat:toqkpb6hzbeghegarpi2vaswcq

Constructs, concepts and criteria for reuse in concurrent object-oriented languages [chapter]

Ulrike Lechner
1998 Lecture Notes in Computer Science  
For reuse in concurrent object-oriented languages we present a set of reuse constructs.  ...  concepts for reuse.  ...  Acknowledgments We are indebted to Christian Lengauer and Martin Wirsing for their support and for many fruitful discussions.  ... 
doi:10.1007/bfb0053590 fatcat:bfsiswrpizh63eeolruvwhwzqu
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