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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] .  ... 
doi:10.34726/1561 fatcat:5o4lrolrgre5vp77udhuvnofmu

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 [14] .  ... 
doi:10.1109/iemdc.2009.5075292 fatcat:ri34wt5x2rad5pag5wjlaekmy4

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).  ... 
doi:10.1016/0304-3975(94)90081-7 fatcat:ah3ikn7r6fapjmj4bsyz2qeqdu

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.  ... 
doi:10.1016/s0195-6698(80)80022-9 fatcat:q3pfv7o4ozbgxinvkgagrll5be

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.  ... 
doi:10.21136/mb.1997.126151 fatcat:dm3kl4ub25ahloyeujavpya3km

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.  ... 
doi:10.1016/j.disc.2012.01.012 fatcat:pdsavtx4aje63nw2ut36bj63ue

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  ... 
doi:10.1007/978-3-642-28717-6_17 fatcat:sir5u6j5vnaide6m3dmscym7yy

Real closed exponential fields

Paola D'Aquino, Julia F. Knight, Salma Kuhlmann, Karen Lange
2012 Fundamenta Mathematicae  
In an extended abstract [20] , 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.  ... 
doi:10.4064/fm219-2-6 fatcat:4rro7hfgvbgb5c33nkuxte23ie

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.  ... 
arXiv:1112.4062v1 fatcat:dnx5afevivaj5fky7542s5aqhi

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  ... 
doi:10.4283/jmag.2017.22.2.306 fatcat:ptchc54xivbknkzidlm4l4fhq4

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 ].  ... 
doi:10.1515/forum-2015-0226 fatcat:xyy2ngudk5cwjaoxhyhzn3ffoi

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 [10] introduced the concept of an inductive lattice of formations in order to adapt lattice-theoretical methods for the investigation of saturated formations.  ... 
doi:10.15446/recolma.v52n2.77156 fatcat:eueu7brddjfmzkzbs56eazkmea

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  ... 
doi:10.1016/0168-0072(94)90047-7 fatcat:uhokyomxmzbklhdsngeuutwqby

On additive partitions of integers

K. Alladi, P. Erdös, V.E. Hoggatt
1978 Discrete Mathematics  
any two distinct members from any one set can never be in U .  ...  Given a linear recurrence integer sequence U={u"}, U-1 =U-1+ u", na1, u,=1, uz >ul, we prove that the set of positive integers can be partitioned uniquely into two disjoint subsets such that the sum of  ...  Theorem 3 . 6 . 6 Let U= ju"1 be a recursive sequence as in Theorem 2 .2 . Let u, = b > 1 . Then if b is even. U is saturated . I f b is odd then U * = U U {b -11 is saturated.  ... 
doi:10.1016/0012-365x(78)90053-5 fatcat:mhnsbbqyijaf5ckhhnokh76pja

Polyunsaturated Posets and Graphs and the Greene-Kleitman Theorem [article]

Glenn G. Chappell
1998 arXiv   pre-print
West showed that the Greene-Kleitman Theorem is best-possible in a strong sense by exhibiting, for each c \ge 4, a poset with longest chain of cardinality c and no k- and l-saturated chain partition for  ...  A chain partition is k-saturated if this bound is achieved. Greene and Kleitman proved that, for each k, every finite poset has a simultaneously k- and k+1-saturated chain partition.  ...  Also, in every 1-saturated chain partition, u lies on the same chain as r 1 , and in every j + 1-saturated chain partition, u lies on the same chain as r j .  ... 
arXiv:math/9807175v1 fatcat:4oh6c5cdrrgshmvohuyukvsamu
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