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Integer Induction in Saturation [article]

Petra Hozzova, Laura Kovacs, Andrei Voronkov
2021
We introduce inference rules for integer induction within the saturation framework of first-order theorem proving.  ...  In this paper we analyze the challenge of automating inductive reasoning with integers.  ...  Induction in saturation-based theorem proving is a new exciting direction in the automation of induction, recently introduced in [5, 10, 16] .  ...

Non linear half-order modeling of synchronous machine

S. Racewicz, D. Riu, N. Retiere, P. Chzran
2009 2009 IEEE International Electric Machines and Drives Conference
Nevertheless, non integer order models have been established under linear conditions. It is than interesting to study the influence of saturation on such model parameters.  ...  Non integer order systems are used to model diffusion in conductive parts of electrical machines as they lead to more compact and knowledge models but also to improve their precision.  ...  Indeed, in electrical machines, magnetic saturation of ferromagnetic pieces influences mainly the value of the inductances  .  ...

A general storage theorem for integers in call-by-name λ-calculus

Jean-Louis Krivine
1994 Theoretical Computer Science
., A general storage theorem for integers in call-by-name /I-calculus, Theoretical Computer Science 129 (1994) 79994. The notion of storage operator introduced in J.-L.  ...  Krivine, 1991 Krivine, , 1990 appears to be an important tool in the study of data types in second-order i-calculus.  ...  By induction on i, we show that ti+ 1 EZ~, for 0 < i < n. This is clear for i =O, since ZO is saturated. If t:EE(il), then 4t:~Z-i and therefore, t:+ 1 E%, because Ei is saturated (1 di<n).  ...

A Partition of L(3, n) into Saturated Symmetric Chains

Bernt Lindström
1980 European journal of combinatorics (Print)
For positive integers m and n let Lim, n) denote the set of all m-tuples (ab az, . . . , am) of integers with Q~al~aZ~···~am~n. The set L(m,n) is partially ordered such that (ab ... , am)~(bb ...  ...  Littlewood assumed that there is such a partition of L(m, n) into symmetric chains for all m, n;;" 1 in his book Theory of Group Characters.  ...  By the induction it is sufficient to give a partition of S; into saturated symmetric chains.  ...

On \$r\$-extendability of the hypercube \$Q\sb n\$

Nirmala B. Limaye, Dinesh G. Sarvate
1997 Mathematica Bohemica
This means that the edges yz,m(xv),m(wk) are parallel in G2. By induction, extend this set to a 1-factor E2 of G2.  ...  The associated integers of these edges are j and i, respectively. All edges in Si U TO(S2) have one end vertex in Lj and the other in £2.  ...

The edge spectrum of the saturation number for small paths

Ronald J. Gould, Wenliang Tang, Erling Wei, Cun-Quan Zhang
2012 Discrete Mathematics
Theorem 1.1 says that a K 3 -saturated graph is either a complete bipartite graph or its size falls in the given range and all values in this range are possible.  ...  A natural aim is to find, if possible, an H-saturated graph with m edges for any integer m between the saturation number and extremal number.  ...  One exception in this table is n = 11, m = 14. There is no such kinds of P 6 -saturated graphs, but for the next induction set we do have a (16, 24)-graph 4K 4 , which is a P 6 -saturated graph.  ...

Automatic Generation of Invariants for Circular Derivations in SUP(LA) [chapter]

Arnaud Fietzke, Evgeny Kruglov, Christoph Weidenbach
2012 Lecture Notes in Computer Science
In this paper, we extend the SUP(LA) calculus with an additional inference rule, automatically generating inductive invariants from partial SUP(LA) derivations.  ...  We have implemented the rule in the SPASS(LA) theorem prover with promising results, showing that it can considerably speed up proof search and enable termination of saturation for practically relevant  ...  As evidenced by our implementation, the constraint induction rule can considerably speed up proof search, enabling termination of saturation in cases where it would otherwise diverge, and allowing shorter  ...

Real closed exponential fields

Paola D'Aquino, Julia F. Knight, Salma Kuhlmann, Karen Lange
2012 Fundamenta Mathematicae
In an extended abstract  , Ressayre considered real closed exponential fields and integer parts that respect the exponential function.  ...  He outlined a proof that every real closed exponential field has an exponential integer part. In the present paper, we give a detailed account of Ressayre's construction.  ...  Recursive saturation has already come up in connection with integer parts.  ...

Real closed exponential fields [article]

Paola D'Aquino, Julia F. Knight, Salma Kuhlmann, Karen Lange
2011 arXiv   pre-print
In an extended abstract Ressayre considered real closed exponential fields and integer parts that respect the exponential function.  ...  He outlined a proof that every real closed exponential field has an exponential integer part.  ...  Recursive saturation has already come up in connection with integer parts.  ...

An Investigation of Induction Motor Saturation under Voltage Fluctuation Conditions

Morteza Ghaseminezhad, Aref Doroudi, Seyed Hossein Hosseinian, Alireza Jalilian
2017 Journal of Magnetics
Nowadays power quality effects on induction motors have gained significant attention due to wide application of these motors in industry.  ...  The degree of iron saturation is a paramount factor affecting induction motors performance.  ...  The saturation harmonics rotate in the air-gap with the same speed and direction as the fundamental frequency, whereas the time and space harmonics create rotating fields with the speed of integer and  ...

On the value group of a model of Peano Arithmetic

Merlin Carl, Paola D'Aquino, Salma Kuhlmann
2017 Forum mathematicum
Countable recursively saturated exponential groups We now investigate recursively saturated real closed fields in light of Theorem 9.  ...  In particular, it is shown that the value group of a recursively saturated real closed field is recursively saturated [DKL, Theorem 5.2 ].  ...

Inductive lattices of totally composition formations

Aleksandr Tsarev
2018 Revista Colombiana de Matemáticas
In this paper, we give a simple proof of the fact that the lattice of all τ-closed totally composition formations of finite groups is inductive.  ...  Let τ be a subgroup functor such that all subgroups of every finite group G contained in τ(G) are subnormal in G.  ...  Skiba  introduced the concept of an inductive lattice of formations in order to adapt lattice-theoretical methods for the investigation of saturated formations.  ...

Classical logic, storage operators and second-order lambda-calculus

Jean-Louis Krivine
1994 Annals of Pure and Applied Logic
We describe here a simple method in order to obtain programs from proofs in second-order classical logic.  ...  Then we extend to classical logic the results about storage operators (typed I-terms which simulate call-by-value in call-by-name) proved by for intuitionistic logic.  ...  Z of n will be said to be c-saturated if it is saturated, and if (t)lx(x)t, . p-equivalent to a Church integer (resp. to the Church integer n), and, as such, will behave as expected when it will occur  ...