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Integer Vector Addition Systems with States
[chapter]

2014
*
Lecture Notes in Computer Science
*

This paper studies reachability, coverability and inclusion problems for

doi:10.1007/978-3-319-11439-2_9
fatcat:7pvckuxbvzfrvkecxg2wqrkaum
*Integer**Vector**Addition**Systems*with States (ZVASS) and extensions and restrictions thereof. ... A ZVASS comprises a finite-state controller with a finite number of counters ranging over the*integers*. ... Z-VASS R ) if A = {λ 1 E 1 + • • • + λ d E d : λ i ∈ {0, 1}, i ∈ [d]}; -*integer**vector**addition**system*with states (Z-VASS) if A = I d ; -*integer**vector**addition**system*(Z-VAS) if A is a Z-VASS and |Q ...##
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Affine Extensions of Integer Vector Addition Systems with States
[article]

2021
*
arXiv
*
pre-print

We study the reachability problem for affine ℤ-VASS, which are

arXiv:1909.12386v3
fatcat:lbo5ldqzajcghjoyhwpszfbgwe
*integer**vector**addition**systems*with states in which transitions perform affine transformations on the counters. ... EXTENSIONS OF*INTEGER**VECTOR**ADDITION**SYSTEMS*WITH STATES1:15 Vol. 17:3 M. ... RaskinVol. 17:3 1:10 AFFINE EXTENSIONS OF*INTEGER**VECTOR**ADDITION**SYSTEMS*WITH STATES1:11 Vol. 17:3 AFFINE EXTENSIONS OF*INTEGER**VECTOR**ADDITION**SYSTEMS*WITH STATES1:13 Vol. 17:3 AFFINE ...##
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Affine Extensions of Integer Vector Addition Systems with States

2018
*
International Conference on Concurrency Theory
*

We study the reachability problem for affine Z-VASS, which are

doi:10.4230/lipics.concur.2018.14
dblp:conf/concur/BlondinHM18
fatcat:yewxxvrt3nemted6mlxfjz5kvq
*integer**vector**addition**systems*with states in which transitions perform affine transformations on the counters. ... hypothesis and by definition of M (σw k ). 2 0 1 8 14:10 Affine Extensions of*Integer**Vector**Addition**Systems*with States Proof of Theorem 1. ... Affine*Integer*VASS An affine*integer**vector**addition**system*with states (affine Z-VASS) is a tuple V = (d, Q, T ) where d ∈ N, Q is a finite set and T ⊆ Q × Z d×d × Z d × Q. Let us fix such a V. ...##
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Adding digit vectors
[article]

2012
*
arXiv
*
pre-print

Our results show that there are at least 2^m-1 different

arXiv:1209.3585v1
fatcat:kiycpfxg7zhahcxo2kgqkv6gay
*additions*of such*vectors*, while there exist only two types of*addition*that we may employ,*addition*with carry and*addition*without carry. ... In this paper, we study the different possibilities to add two*vectors*of digits of a given length m. ... in a hybrid function*system*(see [6] for this notion) cover all possible cases of function*systems*associated with*additions*of digit*vectors*. ...##
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Computer Arithmetic of Numbers, Vectors, Figures and Functions. Algorithms and Hardware

2020
*
Zenodo
*

Multiplication of multidimensional Multiplication of

doi:10.5281/zenodo.3920212
fatcat:2d4ih7xtunb4dcrq6zjjmm43y4
*integer*codes of*vectors*by the base (1.31) \ 86 2.6. Multiplication of*integer*codes of*vectors*by the base (1.30) \ 86 2.7. ... Algebraic*addition*operations of C-codes \ 38 1. Unary operations with*integer*codes -Uni \ 38 2. Unary operations with non-*integer*codes -Unf \ 39 3. ...##
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Efficient Privacy-Preserving Fingerprint-Based Authentication System Using Fully Homomorphic Encryption

2020
*
Security and Communication Networks
*

The proposed

doi:10.1155/2020/4195852
fatcat:7a54ead3rzezvad5s4uw76dd3e
*system*can perform the fingerprint matching process within about 166 seconds (±0.564 seconds) on average. ... To help smartphone users protect their phone, fingerprint-based authentication*systems*(e.g., Apple's Touch ID) have increasingly become popular in smartphones. ... Using this bit-level*addition*, we can expand it to the*addition*between two*integers*. e algorithm implements*addition*between two*integers*using the TFHE library, and it first initializes two carries, ...##
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Vector Arithmetic in the Triangular Grid

2021
*
Entropy
*

The triangular grid is also regular, but it is not a point lattice: it is not closed under

doi:10.3390/e23030373
pmid:33804720
pmcid:PMC8004019
fatcat:2nxvgu6xdvbmzkd7wr4h3kfqb4
*vector*-*addition*, which gives a challenge. ... This*system*is expanded to the plane using restrictions like, at least one of the coordinates is an*integer*and the sum of the three coordinates is in the interval [−1,1]. ... Whenever the translation*vector*is also an*integer**vector*(i.e., it belongs to ℤ 𝟐 ), again a simple*vector**addition*gives the result. ...##
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Creative Mathematics Education

2012
*
Creative Education
*

that results in the construction of the contradiction-free new real number

doi:10.4236/ce.2012.31008
fatcat:qmur2hlkf5avxfhibx6eksimd4
*system*and the complex*vector*plane. ... Critical thinking is consolidated in the critique of current mathematics and its foundations, creativity in the construction of a mathematical space or*system*. ...*Vector**addition*, translation and dot product as well as inversion are introduced here. At all times, both*systems*will be related to experience. ...##
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MOP: Matrix operations program

1979
*
Behavior Research Methods
*

The left-hand side may also be an operand for

doi:10.3758/bf03205701
fatcat:fjkmlnnfkvafflzk6hkiybkawy
*addition*and subtraction. However, it is a fatal error when the result is also an operand in a matrix multiplication.*Integer*Variable*System*. ... Subsequently,*additional*memory is requested from the operating*system*in minimum 1,000-word segments.Installation Notes. ...##
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DIV, FLOOR, CEIL, MOD and STEP Functions in Nested Loop Programs and Linearly Bounded Lattices
[chapter]

1995
*
Algorithms and Parallel VLSI Architectures III
*

The nested loop programs may contain the

doi:10.1016/b978-044482106-5/50024-7
fatcat:p7dbrrolsbeuvdmhf3my22t7zm
*integer*operators:*integer*division, floor, ceil, and modulo, in expressions and the stride, or step size, of for loops may be greater than one. ... We will show the relation between the*integer*division operators in the SAP and linearly bounded lattices in the corresponding DG. ... This decomposition leads to matrices ½ and ¾ , with corresponding variable*vectors*Ã and Ã , respectively. Matrix ¾ defines the lattice*vectors*with the variables of Ã as free variables. ...##
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Reducibilities Among Decision Problems for HNN Groups, Vector Addition Systems and Subsystems of Peano Arithmetic

1983
*
Proceedings of the American Mathematical Society
*

Our purpose is to exhibit reducibilities among decision problems for conjugate powers in HNN groups, reachability sets of

doi:10.2307/2045489
fatcat:2htyg2zndvgy5bmrm3x7uplpma
*vector**addition**systems*and sentences in subsystems of Peano arithmetic, and show ... By a*vector**addition**system*(of dimension n) we mean a pair (d, W), d in A/", IV a finite subset of Z" (where N and Z denote the nonnegative*integers*and*integers*respectively). ... Let VAS denote the class of*vector**addition**systems*and BVAS denote the bounded*vector**addition**systems*(i.e. (d, W) is in BVAS iff R(d,W) is finite). ...##
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Reducibilities among decision problems for HNN groups, vector addition systems and subsystems of Peano arithmetic

1983
*
Proceedings of the American Mathematical Society
*

Our purpose is to exhibit reducibilities among decision problems for conjugate powers in HNN groups, reachability sets of

doi:10.1090/s0002-9939-1983-0715859-8
fatcat:mpkxayca2rh7xjjpcc5bv624fi
*vector**addition**systems*and sentences in subsystems of Peano arithmetic, and show ... By a*vector**addition**system*(of dimension n) we mean a pair (d, W), d in A/", IV a finite subset of Z" (where N and Z denote the nonnegative*integers*and*integers*respectively). ... Let VAS denote the class of*vector**addition**systems*and BVAS denote the bounded*vector**addition**systems*(i.e. (d, W) is in BVAS iff R(d,W) is finite). ...##
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Typing the Numeric Tower
[chapter]

2012
*
Lecture Notes in Computer Science
*

In

doi:10.1007/978-3-642-27694-1_21
fatcat:kzxna5nuxfeb3jdid2kqujtm44
*addition*, the type*system*provides information to the compiler so that it can perform standard numeric optimizations. ... In this paper, we demonstrate how the type*system*of Typed Racket accommodates both a textbook programming style and expressive static checking. ... In*addition*, bounds on range types are static; bounds cannot depend on values, unlike in dependently-typed*systems*. ...##
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Testing additive integrality gaps
[chapter]

2010
*
Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms
*

However, if, in

doi:10.1137/1.9781611973075.98
dblp:conf/soda/EisenbrandHPS10
fatcat:2dx6ruadz5hsxkjpukoylvj4pi
*addition*, the objective is the all-one*vector*, then one can test in polynomial time whether the*additive*gap is bounded by a constant. ... We consider the problem of testing whether the maximum*additive*integrality gap of a family of*integer*programs in standard form is bounded by a given constant. ... function*vector*into account if one wants to have a similar notion for*additive*integrality gaps. ...##
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Testing additive integrality gaps

2012
*
Mathematical programming
*

However, if, in

doi:10.1007/s10107-012-0518-y
fatcat:bvlnwubxwrfurjzfuqea35dv6i
*addition*, the objective is the all-one*vector*, then one can test in polynomial time whether the*additive*gap is bounded by a constant. ... We consider the problem of testing whether the maximum*additive*integrality gap of a family of*integer*programs in standard form is bounded by a given constant. ... function*vector*into account if one wants to have a similar notion for*additive*integrality gaps. ...
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