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

Shojiro Sakata
1988 Journal of symbolic computation
We present an algorithm for finding a 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.  ...

### Logical Consequence Inside Out [chapter]

Denis Bonnay, Dag Westerståhl
2010 Lecture Notes in Computer Science
Conversely, definitions 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

Abe Shenitzer
1955 Proceedings of the American Mathematical Society
If G is defined by a set 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

Abe Shenitzer
1955 Proceedings of the American Mathematical Society
If G is defined by a set 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.  ...

### Symbolic cover minimization of fully I/O specified finite state machines

D. Drusinsky-Yoresh
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.  ...

### Expressiveness and definability in circumscription

Francicleber Martins Ferreira, Ana Teresa Martins
2011 Manuscrito
Finally, using the previous result, we prove that, whenever a 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.  ...

### Minimization of Visibly Pushdown Automata Using Partial Max-SAT [chapter]

Matthias Heizmann, Christian Schilling, Daniel Tischner
2017 Lecture Notes in Computer Science
We define an equivalence 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.  ...

### SPaC

Hamid Shojaei, Twan Basten, Marc Geilen, Phillip Stanley-Marbell
2008 Proceedings of the 6th IEEE/ACM/IFIP international conference on Hardware/Software codesign and system synthesis - CODES/ISSS '08
This paper presents a 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.  ...

### Minimization of Symbolic Transducers [chapter]

Olli Saarikivi, Margus Veanes
2017 Lecture Notes in Computer Science
We evaluate the benefits 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]

Filippo Bonchi, Ugo Montanari
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.  ...

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

Kathi Fisler, Moshe Y. Vardi
1998 Lecture Notes in Computer Science
Bisimulation has potential in this framework because after intersecting the design with the negation 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.  ...

### Recursive spectra of strongly minimal theories satisfying the Zilber Trichotomy

Uri Andrews, Alice Medvedev
2014 Transactions of the American Mathematical Society
We conjecture that for a strongly 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  ...

### Recursive spectra of strongly minimal theories satisfying the Zilber trichotomy [article]

Uri Andrews, Alice Medvedev
2012 arXiv   pre-print
We conjecture that for a strongly 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.  ...

### On Negative Information in Deductive Databases

Marek A. Suchenek, Rajshekhar Sunderraman
1990 Journal of Database Management
This paper provides an overview 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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