Related papers: On the Average Complexity of Moore's State Minimiz…
We study the computational complexity of various problems related to synchronization of weakly acyclic automata, a subclass of widely studied aperiodic automata. We provide upper and lower bounds on the length of a shortest word…
This paper concerns $\mu$-limit sets of cellular automata: sets of configurations made of words whose probability to appear does not vanish with time, starting from an initial $\mu$-random configuration. More precisely, we investigate the…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
We introduce a new complexity measure for finite strings using probabilistic finite-state automata (PFAs), in the same spirit as existing notions employing DFAs and NFAs, and explore its properties. The PFA complexity $A_P(x)$ is the least…
We study the computational complexity of the infinite-horizon discounted-reward Markov Decision Problem (MDP) with a finite state space $|\mathcal{S}|$ and a finite action space $|\mathcal{A}|$. We show that any randomized algorithm needs a…
We prove a general lower bound on the average-case complexity of Shellsort: the average number of data-movements (and comparisons) made by a $p$-pass Shellsort for any incremental sequence is $\Omega (pn^{1 + 1/p)$ for all $p \leq \log n$.…
We address the problem of minimal actuator placement in linear systems so that the volume of the set of states reachable with one unit or less of input energy is lower bounded by a desired value. First, following the recent work of…
In a simple pattern matching problem one has a pattern $w$ and a text $t$, which are words over a finite alphabet $\Sigma$. One may ask whether $w$ occurs in $t$, and if so, where? More generally, we may have a set $P$ of patterns and a set…
Many problems in quantum information theory can be formulated as optimizations over the sequential outcomes of dynamical systems subject to unpredictable external influences. Such problems include many-body entanglement detection through…
We study the complexity of a fundamental algorithm for fairly allocating indivisible items, the round-robin algorithm. For $n$ agents and $m$ items, we show that the algorithm can be implemented in time $O(nm\log(m/n))$ in the worst case.…
This paper presents a lower bound for optimizing a finite sum of $n$ functions, where each function is $L$-smooth and the sum is $\mu$-strongly convex. We show that no algorithm can reach an error $\epsilon$ in minimizing all functions from…
Finite-state complexity is a variant of algorithmic information theory obtained by replacing Turing machines with finite transducers. We consider the state-size of transducers needed for minimal descriptions of arbitrary strings and, as our…
We prove a general lower bound on the average-case complexity of Shellsort: the average number of data-movements (and comparisons) made by a $p$-pass Shellsort for any incremental sequence is $\Omega (pn^{1 + 1/p})$ for every $p$. The proof…
We examine the reset threshold of randomly generated deterministic automata. We present a simple proof that an automaton with a random mapping and two random permutation letters has a reset threshold of $\mathcal{O}\big( \sqrt{n \log^3 n}…
Linear quantum cellular automata were introduced recently as one of the models of quantum computing. A basic postulate of quantum mechanics imposes a strong constraint on any quantum machine: it has to be unitary, that is its time evolution…
We propose a measure based upon the fundamental theoretical concept in algorithmic information theory that provides a natural approach to the problem of evaluating $n$-dimensional complexity by using an $n$-dimensional deterministic Turing…
In this paper we consider the computational complexity of uniformizing a domain with a given computable boundary. We give nontrivial upper and lower bounds in two settings: when the approximation of boundary is given either as a list of…
An index for a finite automaton is a powerful data structure that supports locating paths labeled with a query pattern, thus solving pattern matching on the underlying regular language. In this paper, we solve the long-standing problem of…
In this paper we consider block languages, namely sets of words having the same length, and study the deterministic and nondeterministic state complexity of several operations on these languages. Being a subclass of finite languages, the…
Asymptotically tight lower bounds are derived for the Input/Output (I/O) complexity of a class of dynamic programming algorithms including matrix chain multiplication, optimal polygon triangulation, and the construction of optimal binary…