Related papers: State Complexity of Testing Divisibility
The complete learning of an $n$-qubit quantum state requires samples exponentially in $n$. Several works consider subclasses of quantum states that can be learned in polynomial sample complexity such as stabilizer states or high-temperature…
In this note a very crude but simple approximation to the set of separable states in an arbitrary simplex of commutative states is given using the fact that on the lines connecting the maximally mixed state and an arbitrary pure state the…
We analyze the complexity of synthesizing random states and unitary operators in a multi-qudit system in two paradigms. In one case, we consider the situation in which we manipulate the system by applying a sequence of one- and two-qudit…
Integer iteration rules such as n |-> {a n + b, c n +d} are studied as minimal examples of the general process of multicomputation. Despite the simplicity of such rules, their multiway graphs can be complex, exhibiting, for example,…
In this paper we introduce a new type of approximate state reductions where the behaviors of the reduced and the original automaton do not have to be identical, but they must match on all words of length less than or equal to some given…
We investigate the state complexity of the permutation operation, or the commutative closure, on Alphabetical Pattern Constraints (APC). This class corresponds to level $3/2$ of the Straubing-Th{\'e}rien Hierarchy and includes the finite,…
Nielsen's approach to quantum state complexity relates the minimal number of quantum gates required to prepare a state to the length of geodesics computed with a certain norm on the manifold of unitary transformations. For a bipartite…
Semiautomata form a rich class of sequence-processing algorithms with applications in natural language processing, robotics, computational biology, and data mining. We establish the first Statistical Query hardness result for semiautomata…
This paper discusses the hardness of finding minimal good-for-games (GFG) Buchi, Co-Buchi, and parity automata with state based acceptance. The problem appears to sit between finding small deterministic and finding small nondeterministic…
Via a multidimensional complementarity relation we derive a novel operational entanglement measure for any discrete quantum system, i.e. for any multidimensional and multipartite system. This new measure admits a separation into different…
We prove the lower bound R(M_m) \geq 3/2 m^2 - 2 on the border rank of m x m matrix multiplication by exhibiting explicit representation theoretic (occurence) obstructions in the sense of the geometric complexity theory (GCT) program. While…
Tile Automata is a recently defined model of self-assembly that borrows many concepts from cellular automata to create active self-assembling systems where changes may be occurring within an assembly without requiring attachment. This model…
A measurement strategy is developed for a new kind of hypothesis testing. It assigns, with minimum probability of error, the state of a quantum system to one or the other of two complementary subsets of a set of N given non-orthogonal…
We analyze the sample complexity of learning from multiple experiments where the experimenter has a total budget for obtaining samples. In this problem, the learner should choose a hypothesis that performs well with respect to multiple…
In this paper, we describe a new method for constructing minimal, deterministic, acyclic finite-state automata from a set of strings. Traditional methods consist of two phases: the first to construct a trie, the second one to minimize it.…
The aim of this paper is twofold. First, we study the number of partitions of a positive integer $m$ into at most $n$ parts in a given set $A$. We prove that such a number is bounded by the $n$-th Fibonacci number $F(n)$ for any $m$ and…
We consider a finite field model of the X-ray transform that integrates functions along lines in dimension 3, within the context of finite fields. The admissibility problem asks for minimal sets of lines for which the restricted transform…
We develop an effective and natural approach to interpret any semigroup admitting a special language of greedy normal forms as an automaton semigroup,namely the semigroup generated by a Mealy automaton encoding the behaviour of such a…
In this paper, we study the statistical difficulty of learning to control linear systems. We focus on two standard benchmarks, the sample complexity of stabilization, and the regret of the online learning of the Linear Quadratic Regulator…
In Formal Languages and Automata Theory courses, students find understanding nondeterministic finite-state and pushdown automata difficult. In many cases, this means that it is challenging for them to comprehend the operational semantics of…