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A necessary condition for a doubly recursive rule to be equivalent to a linear recursive rule

Weining Zhang, C. T. Yu
1987 Proceedings of the 1987 ACM SIGMOD international conference on Management of data - SIGMOD '87  
con&bon for a doubly recursive rule of a certam type to be logically eqmvalent to a smgle lmear recursive rule obtamed m a specific way  ...  Nonlmear recursive quenes are usually less efficient m processmg than lmear recurswe quenes It is therefore of mterest to transform non-lmear recursive quenes mto hnear ones We obtam a necessary and sufficient  ...  @ 1987 ACM O-89791-236-5/87/0005/0345 7% ophnuzmg linear recursive queries 1s that, in the "real world", such quenes are encountered most frequently The nondlstmgulshed vanables may have to be renamed  ... 
doi:10.1145/38713.38751 dblp:conf/sigmod/ZhangY87 fatcat:r5mj5vohbzbyrmkqro5frpubuq

Necessary and sufficient conditions to linearize doubly recursive programs in logic databases

Weining Zhang, Clement T. Yu, Daniel Troy
1990 ACM Transactions on Database Systems  
We provide a set of necessary and sufficient conditions for a simple doubly recursive program to be equivalent to a simple linear recursive program.  ...  If a nonlinear recursive program can be transformed into an equivalent linear recursive program, then it may be computed more efficiently than when the transformation is not possible.  ...  ACKNOWLEDGMENTS We are grateful to Jeffrey Ullman for his comments on an earlier draft of this paper, which led to the discovery of conditions stated in Groups 2 through 5 in Proposition 3.1.  ... 
doi:10.1145/88636.89237 fatcat:6nrtwatouzdjrown2zmbxjw2ou

Some positive results for boundedness of multiple recursive rules [chapter]

Ke Wang
1995 Lecture Notes in Computer Science  
only if it is a unit recursion. (3) The characterization of uniform unboundedness for linear sirups in NS] is extended to a substantial superclass called class C + . (4) Boundedness for class C + with  ...  of equivalent non-recursive programs. (2) A generalized chain program, w h i c h a l l o w IDB predicates of arbitrary arity and remove t h e uniqueness condition of chain variables, is bounded if and  ...  Let Intuitively, e e 0 is a necessary (but not necessarily su cient) condition for an instance produced by e to be mapped to an instance produced by e 0 in any containment mapping between expansions  ... 
doi:10.1007/3-540-58907-4_29 fatcat:jw5xj4ulfzd7bkbio6pe7l4rxm

Page 4533 of Mathematical Reviews Vol. , Issue 91H [page]

1991 Mathematical Reviews  
4533 simple doubly recursive program to be equivalent to a simple linear recursive program. The necessary and sufficient conditions can be verified effectively.” 91h:68037 68P20 Moore, James C.  ...  Using attribute/variable graphs, a necessary and sufficient condition for recursion to be unbounded is presented.  ... 

Linearizing some recursive logic programs

I. Guessarian, J.-E. Pin
1995 IEEE Transactions on Knowledge and Data Engineering  
bodies of the rules is equivalent to a linear program containing at most one recursive call in the bodies of the rules.  ...  We then apply that condition to recursive logic programs containing chain rules: we translate it into a sufficient condition under which a recursive logic program containing n ≥ 2 recursive calls in the  ...  Acknowledgements The authors would like to thank the anonymous referees for their insightful reading and their numerous suggestions to improve the quality of this paper.  ... 
doi:10.1109/69.368513 fatcat:vkztqzhqrfey5fzdqqg64j7nja

Toward a Connectionist Model of Recursion in Human Linguistic Performance

Morten H Christiansen, Nick Chater
1999 Cognitive Science  
Furthermore, we show how a network trained to process recursive structures can also generate such structures in a probabilistic fashion.  ...  This work suggests a novel explanation of people's limited recursive performance, without assuming the existence of a mentally represented competence grammar allowing unbounded recursion. 157  ...  Acknowledgments: We would like to thank James Greeno, Paul Smolensky and an anonymous reviewer for their valuable comments on an earlier version of this manuscript, and Joe Allen, Jim Hoeffner and Mark  ... 
doi:10.1207/s15516709cog2302_2 fatcat:dikvmjlb3zhhnb2fpkojmb3um4

Toward a connectionist model of recursion in human linguistic performance

M Christiansen
1999 Cognitive Science  
Furthermore, we show how a network trained to process recursive structures can also generate such structures in a probabilistic fashion.  ...  This work suggests a novel explanation of people's limited recursive performance, without assuming the existence of a mentally represented competence grammar allowing unbounded recursion. 157  ...  Acknowledgments: We would like to thank James Greeno, Paul Smolensky and an anonymous reviewer for their valuable comments on an earlier version of this manuscript, and Joe Allen, Jim Hoeffner and Mark  ... 
doi:10.1016/s0364-0213(99)00003-8 fatcat:gmwpxosydndcldtx7x2h2eemdm

Bisimulation Equivalence of First-Order Grammars is ACKERMANN-Complete [article]

Petr Jančar, Sylvain Schmitz
2019 arXiv   pre-print
We provide the first known complexity upper bound for this famous problem, in the equivalent setting of first-order grammars.  ...  This ACKERMANN upper bound is optimal, and we also show that strong bisimilarity is primitive-recursive when the number of states of the automata is fixed.  ...  A pushdown system is called real-time if a is restricted to be in Σ, i.e., if no ε transition rules appear in ∆.  ... 
arXiv:1901.07170v1 fatcat:nkfrem6yave6dmom27zakbatlm

On Achieving an Asymptotically Error-Free Fixed-Point of Iterative Decoding for Perfect A Priori Information

J. Kliewer, D. J. Costello
2013 IEEE Transactions on Communications  
For inner codes in a serial concatenation, constituent codes in a parallel concatenation, or variable nodes in doubly-generalized LDPC codes the corresponding encoder condition for acquiring perfect extrinsic  ...  In this paper we provide necessary and sufficient conditions for constituent codes in (multiple) concatenated and graph-based coding schemes to achieve an asymptotically errorfree iterative decoding fixed-point  ...  ACKNOWLEDGMENT The authors wish to thank Pascal Vontobel for contributing the idea of applying the results for the a priori model also to factor graphs.  ... 
doi:10.1109/tcomm.2013.042313.120359 fatcat:f3q7pxmrvfafxfmwicqxykezwe

Undecidable boundedness problems for datalog programs

Gerd G Hillebrand, Paris C Kanellakis, Harry G Mairson, Moshe Y Vardi
1995 The Journal of Logic Programming  
In particular, (1) we use a new generic reduction technique to show that program boundedness is undecidable for arity 2 predicates, even with linear rules; (2) we use the mortality problem of Turing machines  ...  rule, we show that program (resp., predicate) boundedness is undecidable for two linear rules (resp., one rule and a projection) and one initialization rule, where all predicates have small arities (6  ...  We would like to thank the three anonymous reviewers for their many useful comments. Harry G.  ... 
doi:10.1016/0743-1066(95)00051-k fatcat:bsh2dqb6nrhdhiacugw23xdhgi

Combining Horn rules and description logics in CARIN

Alon Y. Levy, Marie-Christine Rousset
1998 Artificial Intelligence  
As a result: we obtain a sound and complete algorithm for reasoning in non-recursive CARIN-ALCMR knowledge bases, and an algorithm for rule subsumption over ALC,d&.  ...  We describe CARIN, a novel family of representation languages, that combine the expressive power of Horn rules and of description logics.  ...  Soundand complete reasoning for non-recursive CARIN-ACCNR When Horn rules are not recursive, they are equivalent to a union of conjunctive queries.  ... 
doi:10.1016/s0004-3702(98)00048-4 fatcat:jxcsl5fmcjhjzlq6k24udtpxem

Symmetry and Integrability of a Reduced, 3-Dimensional Self-Dual Gauge Field Model [article]

C. J. Papachristou
2011 arXiv   pre-print
By using techniques described in a recent paper, the recursion operators for both SDYM3 and PSDYM3 are derived.  ...  By using a non-auto-Backlund transformation, this equation is connected to its potential form (PSDYM3) and a certain isomorphism between the Lie algebras of symmetries of the two systems is shown to exist  ...  In Sec.3, the SDYM3 recursion operator is found in the form of a BT for the linear symmetry condition.  ... 
arXiv:1103.3966v1 fatcat:3yo33sb4arcgthrcuayfpywtr4

Calling context abstraction with shapes

Xavier Rival, Bor-Yuh Evan Chang
2011 SIGPLAN notices  
In essence, we define an abstract interpretation-based analysis framework for recursive programs that permits a fluid per call site abstraction of the call stack-much like how shape analyzers enable a  ...  In this paper, we propose a complementary framework for interprocedural analysis based on a direct abstraction of the calling context.  ...  Acknowledgments We would like to thank Josh Berdine, Noam Rinetzky, and Hongseok Yang for interesting discussions on interprocedural shape analysis and on the issues related to cutpoints.  ... 
doi:10.1145/1925844.1926406 fatcat:zx7d5eqbkzclropcprnbynlymy

Calling context abstraction with shapes

Xavier Rival, Bor-Yuh Evan Chang
2011 Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '11  
In essence, we define an abstract interpretation-based analysis framework for recursive programs that permits a fluid per call site abstraction of the call stack-much like how shape analyzers enable a  ...  In this paper, we propose a complementary framework for interprocedural analysis based on a direct abstraction of the calling context.  ...  Acknowledgments We would like to thank Josh Berdine, Noam Rinetzky, and Hongseok Yang for interesting discussions on interprocedural shape analysis and on the issues related to cutpoints.  ... 
doi:10.1145/1926385.1926406 dblp:conf/popl/RivalC11 fatcat:6z2sqlwi4bgrnnfkzlydrwg3ny

A Shape Graph Logic and A Shape System

Zhao-Peng Li, Yu Zhang, Yi-Yun Chen
2013 Journal of Computer Science and Technology  
Thus, verification conditions could be discharged by general theorem provers.  ...  The proposed shape system requires programmers to provide lightweight shape declarations in recursive structure type declarations.  ...  We also thank the anonymous reviewers for their constructive suggestions and great enthusiasm.  ... 
doi:10.1007/s11390-013-1398-1 fatcat:zfh7ucjamreirkcbh4revj5xlu
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