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Fork algebraic datatypes

P. Martinez Lopez
1998 Logic Journal of the IGPL  
Fork algebras have been proposed as an algebraic basis for the construction of a program synthesis environment.  ...  ; these results make fork algebras a sound and powerful framework for this task.  ...  Abstract fork algebras (AFAs for short) are one attempt to give the algebraic description of proper fork algebras.  ... 
doi:10.1093/jigpal/6.4.531 fatcat:blhhcauarzg5ffy6bicqwrlpwq

Algebraic multigrid fork-form Laplacians

Nathan Bell, Luke N. Olson
2008 Numerical Linear Algebra with Applications  
In this paper we describe an aggregation-based algebraic multigrid method for the solution of discrete k-form Laplacians.  ...  Linear Algebra Appl. 2000; 00:1-6 Prepared using nlaauth.cls  ...  Lastly, we have initiated a study of algebraic multigrid for the Hodge decomposition of general k-forms.  ... 
doi:10.1002/nla.577 fatcat:iqmd4kki2bbl5itvn3xpm4ukca

Forked Temperley-Lieb Algebras and Intermediate Subfactors [article]

Pinhas Grossman
2006 arXiv   pre-print
We consider noncommuting pairs P,Q of intermediate subfactors of an irreducible, finite-index inclusion N in M of II_1 factors such that P and Q are supertransitive with Jones index less than 4 over N. We show that up to isomorphism of the standard invariant, there is a unique such pair corresponding to each even value [P:N]=4cos^2(pi/2n) but none for the odd values [P:N]=4cos^2 (pi/(2n+1)). We also classify the angle values which occur between pairs of intermediate subfactors with small index
more » ... ver their intersection: if [P:N] < 4, then the unique nontrivial angle value is always cos^-1 (1/([P:N]-1)).
arXiv:math/0607335v4 fatcat:ptizx5hn6bbzhbxrxprsxnyt74

Representability and program construction within fork algebras

M. Frias
1998 Logic Journal of the IGPL  
This result makes fork algebras a programming calculus by far more powerful than it was previously thought.  ...  The representation theorem for fork algebras was always misunderstood regarding its applications in program construction.  ...  Proper and Abstract Fork Algebras Proper fork algebras (PFAs for short) are extensions of algebras of binary relations [17] with a new operator called fork, and denoted by ∇.  ... 
doi:10.1093/jigpal/6.2.227 fatcat:4uwwwngqo5e7jedeeq3wsy4uum

Forked Temperley–Lieb algebras and intermediate subfactors

Pinhas Grossman
2007 Journal of Functional Analysis  
I would also like to thank David Evans for pointing out the results on algebras associated to T -graphs.  ...  The forked Temperley-Lieb algebras in the above definition are a special case of algebras associated to T -shaped graphs which were studied by Evans and Gould in [5] .  ...  Subfactors coming from forked Temperley-Lieb algebras Definition We note some properties of the example in the preceeding section. .  ... 
doi:10.1016/j.jfa.2007.03.014 fatcat:mnpedmjglrgo5aua5ljywy626i

th-Forking, Algebraic Independence and Examples of Rosy Theories [article]

Alf Onshuus
2003 arXiv   pre-print
We proved that rosy theories include simple and o-minimal theories and that for any theory for which the stable forking conjecture was true, \th-forking coincides with forking independence.  ...  In this article, we continue to study properties of th-forking and find more examples of rosy theories.  ... 
arXiv:math/0306003v1 fatcat:c7pwohzlnrhnjmiekdtacbdbya

A short proof of representability of fork algebras

Viktor Gyuris
1997 Theoretical Computer Science  
In this paper a strong relationship is demonstrated between fork algebras and quasi-projective relation algebras.  ...  With the help of Tarski's classical representation theorem for quasi-projective relation algebras, a short proof is given for the representation theorem of fork algebras.  ...  the notion pre-fork algebra to denote the class we call here fork algebra.  ... 
doi:10.1016/s0304-3975(96)00299-x fatcat:4cckbcd2mjgsbnekemv52dgvai

Fork-Resilient Cross-Blockchain Transactions through Algebraic Topology [article]

Dongfang Zhao
2020 arXiv   pre-print
However, state-of-the-art CBT models do not address the effect of the possible local fork suspension that might invalidate the entire CBT.  ...  This paper takes an algebraic-topological approach to abstract the blockchains and their transactions into simplicial complexes and shows that CBTs cannot complete in either a committed or an aborted status  ...  We take an algebraic-topological approach to abstract the blockchains and their transactions into simplicial complexes, and show that CBTs cannot complete in either a committed or an aborted status by  ... 
arXiv:2004.08473v2 fatcat:zmelwdyvlvhjvfxz24k6oxcuoa

Fork Algebras as a Sufficiently Rich Universal Institution [chapter]

Carlos G. Lopez Pombo, Marcelo F. Frias
2006 Lecture Notes in Computer Science  
Therefore, formulas are equations and fork is equational reasoning in the theory of fork algebras (to be introduced later). This makes reasoning in fork algebras simple.  ...  Algebraization of computational logics in the theory of fork algebras has been a research topic for a while.  ...  Full Closure Fork algebras Full Closure Fork Algebras with Urelements (denoted by FCFAU) are extensions of relation algebras [12] , that is, they possess a relation algebra reduct.  ... 
doi:10.1007/11784180_19 fatcat:xtppciowrbca3kfwjqhymqcoay

Forking and stability in the representations of a C*-algebra [article]

Camilo Argoty
2012 arXiv   pre-print
We show that the theory of a non-degenerate representation of a C*-algebra A over a Hilbert space H is superstable.  ...  Also, we characterize forking, orthogonality and domination of types and show that the theory has weak elimination of imaginaries.  ...  introduction Let A be a unital C * -algebra and let π : A → B(H) be a C * -algebra nondegenerate isometric homomorphism, where B(H) is the algebra of bounded operators over a Hilbert space H.  ... 
arXiv:1211.7155v1 fatcat:2e3xwfmlobd2vb3caisuwyba74

Algebraic Modelling and Performance Evaluation of Acyclic Fork-Join Queueing Networks [chapter]

Nikolai K. Krivulin
2000 Advances in Stochastic Simulation Methods  
Simple lower and upper bounds on mean cycle time in stochastic acyclic fork-join queueing networks are derived using a (max,+)-algebra based representation of network dynamics.  ...  A (max,+)-algebra representation of the fork-join network dynamics and related examples are given in Section 4.  ...  In this paper we propose an approach to get bounds on the mean cycle time, which exploits the (max,+)-algebra representation of acyclic fork-join network dynamics derived in [8, 9] .  ... 
doi:10.1007/978-1-4612-1318-5_5 fatcat:f3dszexwavhrjofhr4ufwaa4bu

Interpretability of first-order linear temporal logics in fork algebras

Marcelo F. Frias, Carlos G. López Pombo
2006 The Journal of Logic and Algebraic Programming  
In this paper we prove theorems on the interpretability of the first-order temporal logics LT L and T L into fork algebras.  ...  This result is part of a research project on the interpretability of logics in fork algebras, and has important applications towards the relational specification of properties of systems within the Ar  ...  A "proper closure fork algebra on S, T " is a proper closure fork algebra A for which U A = T (S, T ) ૽ , and fork is defined by U ∇ V = { t 1 , t 2 ૽t 3 : t 1 , t 2 ∈ U ∧ t 1 , t 3 ∈ V } .  ... 
doi:10.1016/j.jlap.2005.04.005 fatcat:wq7kq57wxjfc3eocmb3t6susci

Some classes containing a fork algebra equivalent variety involving projections

J. Duran
1998 Logic Journal of the IGPL  
The classes have as a subvariety the abstract fork algebra (AFA) equivalent variety involving projections. They are obtained by weakening some laws valid in AFA.  ...  Finally, the existence of equivalent classes with a binary operation like fork is studied.  ...  For example the comparison of direct products of heterogeneous relation algebras with fork algebras [3] ,groupoid representable fork algebras with set fork algebras [25] and AFA with Q-relation algebras  ... 
doi:10.1093/jigpal/6.2.203 fatcat:njkcxjz5zfhateifoyy2kowzfa

On Previdi's delooping conjecture forK-theory

Sho Saito
2015 Algebra & Number Theory  
His main results are formulated in terms of algebraic K-theory, and he observes a certain relation between the K-groups K i .A/ and K i C1 . lim !  ...  Denote by K the sheaf of group-like E 1 -spaces on the Nisnevich site of Spec R, that sends an étale R-algebra S to the space 1 ‫.ދ‬S /.  ...  Algebra & Number Theory  ... 
doi:10.2140/ant.2015.9.1 fatcat:6ogqgr3qpbaxlgnnruxbekpdne

Squares in Fork Arrow Logic

Renata P. de Freitas, Jorge P. Viana, Mario R. F. Benevides, Sheila R. M. Veloso, Paulo A. S. Veloso
2003 Journal of Philosophical Logic  
FAL is the modal logic of fork algebras (FAs) just as arrow logic is the modal logic of relation algebras (RAs).  ...  A proper FA is an algebra of relations where the fork is induced by an injective operation coding pair formation.  ...  of fork algebras.  ... 
doi:10.1023/a:1024847106313 fatcat:2fpe5w6f3bchzpy575rogr6yyq
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