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Research Output 1980 2019

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2019

Low-complexity computations for nilpotent subgroup problems

Macdonald, J., Miasnikov, A. & Ovchinnikov, D., Jan 1 2019, (Accepted/In press) In : International Journal of Algebra and Computation.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Low Complexity
Subgroup
Straight-line Programs
Normalizer
Nilpotency

Undecidability of equations in free lie algebras

Kharlampovich, O. & Miasnikov, A., Jan 1 2019, In : Transactions of the American Mathematical Society. 371, 4, p. 2987-2999 13 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Free Lie Algebra
Undecidability
Integral domain
Algebra
System of equations
2018

Algebraic geometry over algebraic structures X: Ordinal dimension

Daniyarova, E. Y. E., Miasnikov, A. & Remeslennikov, V. N., Dec 1 2018, In : International Journal of Algebra and Computation. 28, 8, p. 1425-1448 24 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Algebraic Geometry
Algebraic Structure
Krull Dimension
Algebraic Variety
Signature
1 Citation (Scopus)

Characterization of finitely generated groups by types

Miasnikov, A. & Romanovskii, N. S., Dec 1 2018, In : International Journal of Algebra and Computation. 28, 8, p. 1613-1632 20 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Finitely Generated Group
Finitely Generated
Polycyclic Group
Metabelian group
Solvable Group
1 Citation (Scopus)

Divisible Rigid Groups. II. Stability, Saturation, and Elementary Submodels

Miasnikov, A. & Romanovskii, N. S., Mar 1 2018, In : Algebra and Logic. 57, 1, p. 29-38 10 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Elementary Submodel
Divisible
Saturation
Quotient
Quantifier Elimination

Elementary equivalence of rings with finitely generated additive groups

Miasnikov, A., Oger, F. & Sohrabi, M., Jun 1 2018, In : Annals of Pure and Applied Logic. 169, 6, p. 514-522 9 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Finitely Generated
Equivalence
Ring
Finitely Generated Group
Nilpotent Group
2 Citations (Scopus)

Equations in Algebras

Kharlampovich, O. & Miasnikov, A., Dec 1 2018, In : International Journal of Algebra and Computation. 28, 8, p. 1517-1533 17 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Relatively Hyperbolic Groups
Right-angled Artin Group
Free Associative Algebras
Graph of Groups
Torsion-free Group
2 Citations (Scopus)

Tarski-type problems for free associative algebras

Kharlampovich, O. & Miasnikov, A., Apr 15 2018, In : Journal of Algebra. 500, p. 589-643 55 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Free Associative Algebras
Finite Rank
Weak Order
First-order
Ring

The complexity of verbal languages over groups

Jain, S., Miasnikov, A. & Stephan, F., Jan 1 2018, (Accepted/In press) In : Journal of Computer and System Sciences. 101, p. 68-85 18 p.

Research output: Contribution to journalArticle

Formal languages
Context sensitive languages
Context free languages
Pattern Language
Context-free Languages

The Conjugacy Problem in Free Solvable Groups and Wreath Products of Abelian Groups is in TC0

Miasnikov, A., Vassileva, S. & Weiß, A., Feb 12 2018, (Accepted/In press) In : Theory of Computing Systems. p. 1-24 24 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Conjugacy Problem
Wreath Product
Solvable Group
Free Group
Torsional stress

Undecidability of the First Order Theories of Free Noncommutative Lie Algebras

Kharlampovich, O. & Miasnikov, A., Sep 1 2018, In : Journal of Symbolic Logic. 83, 3, p. 1204-1216 13 p.

Research output: Contribution to journalArticle

Noncommutative Algebra
Undecidability
Lie Algebra
First-order
Ring
1 Citation (Scopus)

What does a group algebra of a free group “know” about the group?

Kharlampovich, O. & Miasnikov, A., Jun 1 2018, In : Annals of Pure and Applied Logic. 169, 6, p. 523-547 25 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Group Algebra
Free Group
Second-order Logic
Weak Order
Geodesic
2017
2 Citations (Scopus)

Algebraic Geometry Over Algebraic Structures. VI. Geometrical Equivalence

Daniyarova, E. Y., Miasnikov, A. & Remeslennikov, V. N., Sep 1 2017, In : Algebra and Logic. 56, 4, p. 281-294 14 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Algebraic Geometry
Algebraic Structure
Equivalence
Algebraic Set
Classification Problems
4 Citations (Scopus)

Algorithmically complex residually finite groups

Kharlampovich, O., Miasnikov, A. & Sapir, M., Aug 1 2017, In : Bulletin of Mathematical Sciences. 7, 2, p. 309-352 44 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Residually Finite Groups
Dehn Function
Recursive Functions
Class

Amenability of Schreier graphs and strongly generic algorithms for the conjugacy problem

Diekert, V., Miasnikov, A. & Weiß, A., Nov 1 2017, In : Journal of Symbolic Computation. 83, p. 147-165 19 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Conjugacy Problem
Amenability
HNN Extension
Polynomials
Graph in graph theory

Computational complexity and the conjugacy problem

Miasnikov, A. & Schupp, P., Jan 1 2017, In : Computability. 6, 4, p. 307-318 12 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Conjugacy Problem
Computational complexity
Computational Complexity
Mirrors
Linear Time
Finitely Generated Group
Nilpotent Group
Torsion-free
Torsion-free Group
Heisenberg Group

Log-space conjugacy problem in the Grigorchuk group

Miasnikov, A. & Vassileva, S., May 1 2017, In : Groups, Complexity, Cryptology. 9, 1, p. 77-85 9 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Conjugacy Problem
Space Complexity
1 Citation (Scopus)

Model-Theoretic Aspects of the Theory of Divisible Rigid Soluble Groups

Miasnikov, A. & Romanovskii, N. S., Mar 1 2017, In : Algebra and Logic. 56, 1, p. 82-84 3 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

1 Citation (Scopus)

Random nilpotent groups, polycyclic presentations, and Diophantine problems

Garreta, A., Miasnikov, A. & Ovchinnikov, D., Nov 1 2017, In : Groups, Complexity, Cryptology. 9, 2, p. 99-115 17 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Nilpotent Group
Torsional stress
Torsion-free
Finitely Generated
Presentation

Stallings graphs for quasi-convex subgroups

Kharlampovich, O., Miasnikov, A. & Weil, P., Oct 15 2017, In : Journal of Algebra. 488, p. 442-483 42 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Quasiconvex
Subgroup
Graph in graph theory
Relatively Hyperbolic Groups
Right-angled Artin Group
1 Citation (Scopus)

Universal geometrical equivalence of the algebraic structures of common signature

Daniyarova, E. Y., Miasnikov, A. & Remeslennikov, V. N., Sep 1 2017, In : Siberian Mathematical Journal. 58, 5, p. 801-812 12 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Algebraic Structure
Signature
Equivalence
Algebraic Geometry
Affine transformation
Stable Map
Bilinear Map
Structure Theorem
Nilpotent Group
Algebraic Structure
2016

Conjugacy in Baumslag’s Group, Generic Case Complexity, and Division in Power Circuits

Diekert, V., Miasnikov, A. & Weiß, A., Dec 1 2016, In : Algorithmica. 76, 4, p. 961-988 28 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Conjugacy Problem
Conjugacy
Division
Computability and decidability
Networks (circuits)

Generic case completeness

Miasnikov, A. & Ushakov, A., Dec 1 2016, In : Journal of Computer and System Sciences. 82, 8, p. 1268-1282 15 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Completeness
Computational complexity
NP-complete problem
Halting Problem
3 Citations (Scopus)

Non-commutative lattice problems

Miasnikov, A., Nikolaev, A. & Ushakov, A., May 1 2016, In : Journal of Group Theory. 19, 3, p. 455-475 21 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Subgroup
Coxeter Group
Nilpotent Group
Free Group
Polynomial-time Algorithm

Quadratic equations in the grigorchuk group

Lysenok, I., Miasnikov, A. & Ushakov, A., Jan 1 2016, In : Groups, Geometry, and Dynamics. 10, 1, p. 201-239 39 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Quadratic equation
Commutator
Corollary
2015
9 Citations (Scopus)

A linear decomposition attack

Miasnikov, A. & Roman'Kov, V., May 1 2015, In : Groups, Complexity, Cryptology. 7, 1, p. 81-94 14 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Cryptography
Attack
Polynomials
Decomposition
Decompose
1 Citation (Scopus)

Generic Theories as a Method for Approximating Elementary Theories

Miasnikov, A. & Remeslennikov, V. N., Jan 1 2015, In : Algebra and Logic. 53, 6, p. 512-519 8 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Groups acting on hyperbolic-metric spaces

Grecianu, A. P., Kvaschuk, A. V., Miasnikov, A. & Serbin, D., Sep 1 2015, In : International Journal of Algebra and Computation. 25, 6, p. 977-1042 66 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Hyperbolic Metric
Metric space
Group Action
Hyperbolic Structure
Ordered Group

On asymptotic properties of verbal subsets in a group

Miasnikov, A. & Roman’kov, V., Oct 1 2015, In : Lobachevskii Journal of Mathematics. 36, 4, p. 399-402 4 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Asymptotic Density
Free Group
Asymptotic Properties
Exponent
Subset
2014
1 Citation (Scopus)

Dimension in universal algebraic geometry

Daniyarova, E. Y., Miasnikov, A. & Remeslennikov, V. N., Jan 1 2014, In : Doklady Mathematics. 90, 1, p. 450-452 3 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

1 Citation (Scopus)

Diophantine cryptography in free metabelian groups: Theoretical base

Miasnikov, A. & Roman'Kov, V., Nov 1 2014, In : Groups, Complexity, Cryptology. 6, 2, p. 103-120 18 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Metabelian group
Free Group
Cryptography
Endomorphism
Hardness
4 Citations (Scopus)

Finitely presented expansions of groups, semigroups, and algebras

Khoussainov, B. & Miasnikov, A., Jan 2 2014, In : Transactions of the American Mathematical Society. 366, 3, p. 1455-1474 20 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Algebra
Semigroup
Finitely Generated
Computer science
Equality
15 Citations (Scopus)

From automatic structures to automatic groups

Kharlampovich, O., Khoussainov, B. & Miasnikov, A., Jan 1 2014, In : Groups, Geometry, and Dynamics. 8, 1, p. 157-198 42 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Graph in graph theory
Metabelian group
Word problem
Free Product
Cayley Graph
1 Citation (Scopus)

Infinite words and universal free actions

Kharlampovich, O., Miasnikov, A. & Serbin, D., Jan 1 2014, In : Groups, Complexity, Cryptology. 6, 1, p. 55-69 15 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Free Action
Infinite Words
Ordered Group
Group Action
Abelian group
14 Citations (Scopus)

Knapsack problems in groups

Miasnikov, A., Nikolaev, A. & Ushakov, A., Jan 1 2014, In : Mathematics of Computation. 84, 292, p. 987-1016 30 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Knapsack Problem
Subset Sum Problem
Computational complexity
Finitely Presented Groups
Hyperbolic Groups
4 Citations (Scopus)

Logical aspects of the theory of divisible rigid groups

Miasnikov, A. & Romanovskii, N. S., Jan 1 2014, In : Doklady Mathematics. 90, 3, p. 697-698 2 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Tame Automorphisms of Elementary Free Groups

Fine, B., Kharlampovich, O. G., Miasnikov, A., Remeslennikov, V. N. & Rosenberger, G., Aug 1 2014, In : Communications in Algebra. 42, 8, p. 3386-3394 9 p.

Research output: Contribution to journalArticle

Free Group
Automorphism Group
Finitely Generated
Automorphisms
4 Citations (Scopus)

The Post correspondence problem in groups

Miasnikov, A., Nikolaev, A. & Ushakov, A., Nov 1 2014, In : Journal of Group Theory. 17, 6, p. 981-1008 28 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Correspondence Problem
Word problem
Free Group
Conjugacy Problem
Polynomial time
8 Citations (Scopus)

Verbally closed subgroups of free groups

Miasnikov, A. & Roman'Kov, V., Jan 1 2014, In : Journal of Group Theory. 17, 1, p. 29-40 12 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Retract
Finite Rank
Free Group
Subgroup
Closed
2 Citations (Scopus)
Relatively Hyperbolic Groups
Hyperbolic Groups
Subgroup
Class
2013
10 Citations (Scopus)

Definable sets in a hyperbolic group

Kharlampovich, O. & Miasnikov, A., Feb 1 2013, In : International Journal of Algebra and Computation. 23, 1, p. 91-110 20 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Hyperbolic Groups
Torsion-free
Corollary
Subgroup
8 Citations (Scopus)

On Rationality of Verbal Subsets in a Group

Miasnikov, A. & Roman'kov, V., Jan 1 2013, In : Theory of Computing Systems. 52, 4, p. 587-598 12 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Rationality
Subset
Free Product
If and only if
Generalise
2012
12 Citations (Scopus)

Algebraic geometry over algebraic structures. II. Foundations

Daniyarova, E. Y., Miasnikov, A. & Remeslennikov, V. N., Aug 1 2012, In : Journal of Mathematical Sciences (United States). 185, 3, p. 389-416 28 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Algebraic Set
Algebraic Geometry
Algebraic Structure
Unification
Algebra
10 Citations (Scopus)

Algebraic geometry over algebraic structures. V. The case of arbitrary signature

Daniyarova, E. Y., Miasnikov, A. & Remeslennikov, V. N., Mar 1 2012, In : Algebra and Logic. 51, 1, p. 28-40 13 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Algebraic Geometry
Algebraic Structure
Signature
Arbitrary
Predicate

Amalgamated free product of groups: Normal forms and measures

Miasnikov, A., Remeslennikov, V. N. & Frenkel', E. V., Apr 1 2012, In : Mathematical Notes. 91, 3-4, p. 592-596 5 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Amalgamated products of groups: Measures of random normal forms

Miasnikov, A., Remeslennikov, V. N. & Frenkel, E. V., Jul 27 2012, In : Journal of Mathematical Sciences (United States). 185, 2, p. 300-320 21 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Normal Form
Asymptotic Density
Asymptotic Estimates
Finite Rank
Free Group
2 Citations (Scopus)

Cyclic rewriting and conjugacy problems

Diekert, V., Duncan, A. & Miasnikov, A., Dec 1 2012, In : Groups, Complexity, Cryptology. 4, 2, p. 321-355 35 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Conjugacy Problem
Rewriting
Equivalence classes
Free Product with Amalgamation
HNN Extension

Group extensions over infinite words

Diekert, V. & Miasnikov, A., Aug 1 2012, In : International Journal of Foundations of Computer Science. 23, 5, p. 1001-1019 19 p.

Stevens Institute of Technology

Research output: Contribution to journalArticle

Group theory
String theory
Polynomials