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Fork algebraic datatypes
1998
Logic Journal of the IGPL
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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
2008
Numerical Linear Algebra with Applications
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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]
2006
arXiv
pre-print
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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
arXiv:math/0607335v4
fatcat:ptizx5hn6bbzhbxrxprsxnyt74
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... ver their intersection: if [P:N] < 4, then the unique nontrivial angle value is always cos^-1 (1/([P:N]-1)).
Representability and program construction within fork algebras
1998
Logic Journal of the IGPL
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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
2007
Journal of Functional Analysis
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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]
2003
arXiv
pre-print
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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
1997
Theoretical Computer Science
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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]
2020
arXiv
pre-print
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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]
2006
Lecture Notes in Computer Science
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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]
2012
arXiv
pre-print
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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]
2000
Advances in Stochastic Simulation Methods
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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
2006
The Journal of Logic and Algebraic Programming
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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
1998
Logic Journal of the IGPL
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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
2015
Algebra & Number Theory
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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
2003
Journal of Philosophical Logic
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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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