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Finding a minimal set of linear recurring relations capable of generating a given finite two-dimensional array

1988
*
Journal of symbolic computation
*

We present an algorithm for finding a

doi:10.1016/s0747-7171(88)80033-6
fatcat:gqhfayx2sjbqtam3ugm4jyi4ju
*minimal*set*of*two-dimensional linear recurring*relations*capable*of*generating a prescribed finite two-dimensional array. ... Furthermore, we make clear some relationship between our algorithm and Gr~ibner bases*of*bivariate polynomial ideals, where polynomiaIs correspond one-to-one to linear recurring*relations*. ... This research has been made on the fellowship*of*the exchange programme between the Japanese Society for Promotion*of*Science and the Austrian Academy*of*Science. ...##
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Logical Consequence Inside Out
[chapter]

2010
*
Lecture Notes in Computer Science
*

Conversely, definitions

doi:10.1007/978-3-642-14287-1_20
fatcat:2zd7yeurszhorgpjppi63bn24a
*of*logical consequence can be construed as providing us with mappings from sets*of**symbols*(the ones selected as logical constants) to consequence*relations*. 3 Extraction*of*constants ... The idea for extracting logical constants from a consequence*relation*is the following: they are the*symbols*which are essential to the validity*of*at least one inference, in the sense that replacing them ... X is*minimal*iff for all u ∈ X, ⇒ X = ⇒ X−{u} . Proposition 3. X is*minimal*iff no proper subset*of*X generates the same consequence*relation*. ...##
###
Decomposition of a Group with a Single Defining Relation into a Free Product

1955
*
Proceedings of the American Mathematical Society
*

If G is defined by a set

doi:10.2307/2032354
fatcat:k7de3kmdebhrnggk66e7hmjbo4
*of*prescribed*relations*for the a" G' can be defined by transcribing the original*relations*in terms*of*the A_1a,. ... A word W is said to be active (inactive) T if one (none)*of*its*symbols*is active T. (9)*Minimal*words. ...##
###
Decomposition of a group with a single defining relation into a free product

1955
*
Proceedings of the American Mathematical Society
*

If G is defined by a set

doi:10.1090/s0002-9939-1955-0069174-1
fatcat:owie5hq7xvfpjkorf5vkgqmeym
*of*prescribed*relations*for the a" G' can be defined by transcribing the original*relations*in terms*of*the A_1a,. ... A word W is said to be active (inactive) T if one (none)*of*its*symbols*is active T. (9)*Minimal*words. ...##
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Symbolic cover minimization of fully I/O specified finite state machines

1990
*
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
*

*Symbolic*cover

*minimization*is an important step within a well-known state-assignment technique for finite state machines (FSM's) 121. ... We show a simplified technique, based on an extension

*of*the FSM

*minimization*technique, which enables an efficient deterministic solution for fully I/O specified FSM's. ... A minimum

*symbolic*cover is one

*of*minimum cardinality, i.e., consisting

*of*a minimum number

*of*

*symbolic*implicants.

*Symbolic*

*minimization*consists

*of*finding such a minimum

*symbolic*cover. ...

##
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Expressiveness and definability in circumscription

2011
*
Manuscrito
*

Finally, using the previous result, we prove that, whenever a

doi:10.1590/s0100-60452011000100011
fatcat:nqqtilsd3za3zc6dtpobn44uue
*relation*P i is defined in the class*of*P ; Z-*minimal*models*of*a firstorder sentence φ and whenever such class*of*P ; Z-*minimal*models is ... ∆-elementary, then there is an explicit definition ψ for P i such that the class*of*P ; Z-*minimal*models*of*φ is the class*of*models*of*φ ∧ ψ. ... An example*of*this case occurs when S = {P }, which means that all*relation**symbols*in the*symbol*set are*minimized*. ...##
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Minimization of Visibly Pushdown Automata Using Partial Max-SAT
[chapter]

2017
*
Lecture Notes in Computer Science
*

We define an equivalence

doi:10.1007/978-3-662-54577-5_27
fatcat:eu6vsqt45jhm3cunyu2vlaiooy
*relation*that is sufficient for language-preserving quotienting*of*VPA. ... We encode the existence*of*such a*relation*as a Boolean partial maximum satisfiability (PMax-SAT) problem and present an algorithm that quickly finds satisfying assignments. ... Property (i)*of*a Raq*relation*). Computing quotienting*relations*In Section 3, we introduced the notion*of*a Raq*relation*and showed how we can use it to*minimize*Vpa while preserving the language. ...
This paper presents a

doi:10.1145/1450135.1450176
dblp:conf/codes/ShojaeiBGS08
fatcat:kt3osol2czfanbdkgtjfpgxp6i
*symbolic*Pareto calculator, SPaC, for the algebraic computation*of*multidimensional trade-offs. SPaC uses BDDs as a representation for solution sets and operations on them. ... The tool can be used in multi-criteria optimization and design-space exploration*of*embedded systems. ...*Symbolic**Minimization*It remains to discuss a*symbolic**minimization*algorithm. The*minimization*operation extracts the Pareto configurations from a particular configuration set. ...##
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Minimization of Symbolic Transducers
[chapter]

2017
*
Lecture Notes in Computer Science
*

We evaluate the benefits

doi:10.1007/978-3-319-63390-9_10
fatcat:vtzv2nqavvbtdm3qeh3qtnwb44
*of*the proposed algorithm over real-world stream processing computations where*symbolic*transducers are formed as a result*of*repeated compositions. ... Here we develop the theory for and an algorithm for computing quotients*of*such transducers under indistinguishability preserving equivalence*relations*over states such as bisimulation. ...*Minimization**of**symbolic*automata. ...##
###
Page 277 of American Mathematical Society. Proceedings of the American Mathematical Society Vol. 6, Issue 2
[page]

1955
*
American Mathematical Society. Proceedings of the American Mathematical Society
*

*of*the defining

*relation*associated with this representation contains at most n—1

*symbols*. ... By the corollary to our lemma every

*minimal*form

*of*R contains n distinct

*symbols*. ...

##
###
Minimization Algorithm for Symbolic Bisimilarity
[chapter]

2009
*
Lecture Notes in Computer Science
*

*Symbolic*semantics allows to define smaller, possibly finite, transition systems, by employing

*symbolic*actions and avoiding some sources

*of*infiniteness. ... Unfortunately, the standard partition refinement algorithm does not work with

*symbolic*bisimilarity. ... This is the

*minimal*

*symbolic*automaton

*of*l. Notice that it is isomorphic to the

*symbolic*transition system

*of*a ( Fig.1(C) ). This is an alternative proof

*of*a ∼ S l. ...

##
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Bisimulation Minimization in an Automata-Theoretic Verification Framework
[chapter]

1998
*
Lecture Notes in Computer Science
*

Bisimulation has potential in this framework because after intersecting the design with the negation

doi:10.1007/3-540-49519-3_9
fatcat:f6mgmsyoerfjhhw3uingt7whry
*of*the property,*minimization*can ignore most*of*the atomic propositions. ... It is considered impractical for*symbolic*model checking, however, because the required BDDs are prohibitively large for most designs. ...*Related*Work Several researchers have explored*symbolic**minimization*techniques. ...##
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Recursive spectra of strongly minimal theories satisfying the Zilber Trichotomy

2014
*
Transactions of the American Mathematical Society
*

We conjecture that for a strongly

doi:10.1090/s0002-9947-2014-05897-2
fatcat:otoxtwbouvhqzjrvapsyglgf7i
*minimal*theory T in a finite signature satisfying the Zilber Trichotomy, there are only three possibilities for the recursive spectrum*of*T : all countable models*of*T ... are recursively presentable; none*of*them are recursively presentable; or only the zero-dimensional model*of*T is recursively presentable. ... Setup recap: We have a recursive strongly*minimal*modular groupM in a finite*relational*signatureL which consists*of*the ternary*relation*+ along with a set S*of*binary*relation**symbols*interpreted as ...##
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Recursive spectra of strongly minimal theories satisfying the Zilber trichotomy
[article]

2012
*
arXiv
*
pre-print

We conjecture that for a strongly

arXiv:1104.4666v3
fatcat:sezphceo4bcnblkfyh74qbosri
*minimal*theory T in a finite signature satisfying the Zilber Trichotomy, there are only three possibilities for the recursive spectrum*of*T: all countable models*of*T ... are recursively presentable; none*of*them are recursively presentable; or only the zero-dimensional model*of*T is recursively presentable. ... •T proves that each*relation**symbol*inL is a connected group.• L andL have the same number*of**relation**symbols**of*each Morley rank. ...##
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On Negative Information in Deductive Databases

1990
*
Journal of Database Management
*

This paper provides an overview

doi:10.4018/jdm.1990070103
fatcat:zlobe4zujzbj3iihylks2hkfxq
*of*deductive data bases, with an emphasis on problems*related*to negative information. ... It embeds this subject into a wider context*of*logic programming, exposing certain peculiarities pertinent to treatment*of*negation in these fields. ... Models having larger*relations*, as e.g. one which interprets*symbol*Male as {< M arek >, < F ay >}, and*symbol*Female as {< M arek >, < F ay >}, are not*minimal*. ...
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