Papers by Amnon Rosenmann
Groups - Complexity - Cryptology, 2000
A subgroup H of a free group F is called inert in F if rk(H ∩ G) ≤ rk(G) for every G < F. In this... more A subgroup H of a free group F is called inert in F if rk(H ∩ G) ≤ rk(G) for every G < F. In this paper we expand the known families of inert subgroups. We show that the inertia property holds for 1-generator endomorphisms. Equivalently, echelon subgroups in free groups are inert. An echelon subgroup is defined through a set of generators that are in echelon form with respect to some ordered basis of the free group, and may be seen as a generalization of a free factor. For example, the fixed subgroups of automorphisms of finitely generated free groups are echelon subgroups. The proofs follow mostly a graph-theoretic or combinatorial approach.
Circular automata synchronize with high probability
Journal of Combinatorial Theory, Series A
Linear Algebra and its Applications
Recently, in a work that grew out of their exploration of interlacing polynomials, Marcus, Spielm... more Recently, in a work that grew out of their exploration of interlacing polynomials, Marcus, Spielman and Srivastava [21] and Marcus [20] studied certain combinatorial polynomial convolutions. These convolutions preserve real-rootedness and capture expectations of characteristic polynomials of unitarily invariant random matrices, thus providing a link to free probability. We explore analogues of these types of convolutions in the setting of max-plus algebra. In this setting the max-permanent replaces the determinant, the maximum is the analogue of the expected value and real-rootedness is replaced by full canonical form. Our results resemble those of Marcus et al., however, in contrast to the classical setting we obtain an exact and simple description of all roots of the convolution of p(x) and q(x) in terms of the roots of p(x) and q(x).
Journal of Applied Logic
We present a novel approach, which is based on multiple-valued logic (MVL), to the verification a... more We present a novel approach, which is based on multiple-valued logic (MVL), to the verification and analysis of digital hardware designs, which extends the common ternary or quaternary approaches for simulations. The simulations which are performed in the more informative MVL setting reveal details which are either invisible or harder to detect through binary or ternary simulations. In equivalence verification, detecting different behavior under MVL simulations may lead to the discovery of a genuine binary nonequivalence or to a qualitative gap between two designs. The value of a variable in a simulation may hold information about its degree of truth and its "place of birth" and "date of birth". Applications include equivalence verification, initialization, assertions generation and verification, partial control on the flow of data by prioritizing and block-oriented simulations. Much of the paper is devoted to theoretical aspects behind the MVL approach, including the reason for choosing a specific algebra for computations, and the introduction of the verification complexity of a Boolean expression. Two basic algorithms are presented.
SUBGROUPS OF FINITE INDEX AND THE fc-LOCALIZATION
Commun Algebra, 2001
ABSTRACT
We present a novel approach, which is based on multiple-valued logic (MVL), to the verification a... more We present a novel approach, which is based on multiple-valued logic (MVL), to the verification and analysis of digital hardware designs, which extends the common ternary or quaternary approaches for simulations. The simulations which are performed in the more informative MVL setting reveal details which are either invisible or harder to detect through binary or ternary simulations. In equivalence verification, detecting different behavior under MVL simulations may lead to the discovery of a genuine binary nonequivalence or to a qualitative gap between two designs. The value of a variable in a simulation may hold information about its degree of truth and its "place of birth" and "date of birth". Applications include equivalence verification, initialization, assertions generation and verification, partial control on the flow of data by prioritizing and block-oriented simulations. Much of the paper is devoted to theoretical aspects behind the MVL approach, including the reason for choosing a specific algebra for computations, and the introduction of the verification complexity of a Boolean expression. Two basic algorithms are presented.
Lecture Notes in Computer Science, 2015
Deterministic timed automata are strictly less expressive than their nondeterministic counterpart... more Deterministic timed automata are strictly less expressive than their nondeterministic counterparts, which are again less expressive than those with silent transitions. As a consequence, timed automata are in general non-determinizable. This is unfortunate since deterministic automata play a major role in model-based testing, observability and implementability. However, by bounding the length of the traces in the automaton, effective determinization becomes possible. We propose a novel procedure for bounded determinization of timed automata. The procedure unfolds the automata to bounded trees, removes all silent transitions and determinizes via disjunction of guards. The proposed algorithms are optimized to the bounded setting and thus are more efficient and can handle a larger class of timed automata than the general algorithms. We show how to apply the approach in a fault-based test-case generation method, called model-based mutation testing, that was previously restricted to deterministic timed automata. The approach is implemented in a prototype tool and evaluated on several scientific examples and one industrial case study. To our best knowledge, this is the first implementation of this type of procedure for timed automata.
When Schreier transversals grow wild
Groups St Andrews 1997 in Bath, 2000
Almost Periodicity and the Timetamp of Timed Automata
Given a member A of the class of non-deterministic timed automata with silent transitions (eNTA),... more Given a member A of the class of non-deterministic timed automata with silent transitions (eNTA), we effectively compute its timestamp: the set of all pairs (time value, action) of all observable timed traces of A, a generalization of the reachability problem. We show that the timestamp is eventually periodic and that one can compute a simple deterministic timed automaton with the same timestamp as that of A. As a consequence, we have a partial method, not bounded by time or number of steps, for the general language non-inclusion problem for eNTA. We also show that the language of A is periodic with respect to suffixes.
Idealizers of fractal ideals in free group algebras
The Timestamp of Timed Automata
ABSTRACT
Seventh IEEE International High-Level Design Validation and Test Workshop, 2002., 2002
Combinatorial and Geometric Group Theory, Edinburgh 1993, 1994
The cogrowth of a subgroup is defined as the growth of a set of coset representatives which are o... more The cogrowth of a subgroup is defined as the growth of a set of coset representatives which are of minimal length. A subgroup is essential if it intersects non-trivially every non-trivial subgroup. The main result of this paper is that every function f : N ∪ {0}−→N which is strictly increasing, but at most exponential, is equivalent to a cogrowth function of an essential subgroup of infinite index of the free group of rank two. This class of functions properly contains the class of growth functions of groups. The notions of growth and cogrowth of right ideals in algebras are introduced. We show that when the algebra is without zero divisors then every right ideal, whose cogrowth is less than that of the algebra, is essential.
Computational and Geometric Aspects of Modern Algebra, 2000
Pacific Journal of Mathematics, 1994
The topology defined by all finite codimensional right ideals has interesting properties in the c... more The topology defined by all finite codimensional right ideals has interesting properties in the case of the free algebra and the group ring of a free group. Its open ideals are precisely the finitely generated essential ones. Finitely generated right ideals are closed and the Leavitt numbers of the associated localization are 1 and n-1. The proofs are, for the most part, applications of Schreier's method.
An Algorithm for Constructing Gröbner and Free Schreier Bases in Free Group Algebras
Journal of Symbolic Computation, 1993
Israel Journal of Mathematics, 1997
On Rank, Root and Equations in Free Groups
International Journal of Algebra and Computation, 2001
Let h1, h2,… be a sequence of elements in a free group and let H be the subgroup they generate. L... more Let h1, h2,… be a sequence of elements in a free group and let H be the subgroup they generate. Let H′ be the subgroup generated by w1, w2, …, where each wi is a word in hi and possibly other hj, such that the associated directed graph has the finite paths property. We show that rank H′≥ rank H. As a corollary we get that [Formula: see text], where [Formula: see text] is the subgroup generated by the roots of the elements in H. If H0 is finitely generated and the sequence of subgroups H0, H1, H2, … satisfies [Formula: see text] then the sequence stabilizes, i.e. for some m, Hi=Hi+1 for every i≥ m. When applied to systems of equations in free groups, we give conditions on a transformation of the system such that the maximal rank of a solution (the inner rank) does not increase. In particular, we show that if in "Lyndon equation" [Formula: see text] the exponents ai satisfy gcd (a1,…,an)≠1 then the inner rank is ⌊ n/2⌋. The proofs are mostly elementary.
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Papers by Amnon Rosenmann