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It is well known that computing a minimum DFA consistent with a given set of positive and negative examples is NP-hard. Previous work has identified conditions on the input sample under which the problem becomes tractable or remains hard.…
We consider a random walk on a discrete connected graph having some infinite branches plus finitely many vertices with finite degrees. We find the generator of a strong stationary dual in the sense of Fill, and use it to find some…
The automatic complexity of a finite word (string) is an analogue for finite automata of Sipser's distinguishing complexity (1983) and was introduced by Shallit and Wang (2001). For a finite alphabet $\Sigma$ of at least two elements, we…
Let $X_1,X_2,\ldots $ be independent random variables observed sequentially and such that $X_1,\ldots,X_{\theta-1}$ have a common probability density $p_0$, while $X_\theta,X_{\theta+1},\ldots $ are all distributed according to $p_1\neq…
In this note, we provide complexity characterizations of model checking multi-pushdown systems. Multi-pushdown systems model recursive concurrent programs in which any sequential process has a finite control. We consider three standard…
Sequential parametrized topological complexity is a numerical homotopy invariant of a fibration, which arose in the robot motion planning problem with external constraints. In this paper, we study sequential parametrized topological…
While Kolmogorov complexity is the accepted absolute measure of information content of an individual finite object, a similarly absolute notion is needed for the relation between an individual data sample and an individual model summarizing…
Optimization is an important module of modern machine learning applications. Tremendous efforts have been made to accelerate optimization algorithms. A common formulation is achieving a lower loss at a given time. This enables a…
We consider the problem of learning temporal logic formulas from examples of system behavior. Learning temporal properties has crystallized as an effective mean to explain complex temporal behaviors. Several efficient algorithms have been…
Here we study the computational complexity of the constrained synchronization problem for the class of regular commutative constraint languages. Utilizing a vector representation of regular commutative constraint languages, we give a full…
Kolmogorov complexity of a finite binary word reflects both algorithmic structure and the empirical distribution of symbols appearing in the word. Words with symbol frequencies far from one half have smaller combinatorial richness and…
We bound the future loss when predicting any (computably) stochastic sequence online. Solomonoff finitely bounded the total deviation of his universal predictor M from the true distribution m by the algorithmic complexity of m. Here we…
In Monoidal Computer I, we introduced a categorical model of computation where the formal reasoning about computability was supported by the simple and popular diagrammatic language of string diagrams. In the present paper, we refine and…
In this article we formally define and investigate the computational complexity of the Definability Problem for open first-order formulas (i.e., quantifier free first-order formulas) with equality. Given a logic $\mathbf{\mathcal{L}}$, the…
We give an explicit formula for the time projection in an arbitrary von Neumann algebra from which all its basic properties can be easily derived. The analysis of the situation when this time projection is a conditional expectation is also…
Muchnik's theorem about simple conditional descriptions states that for all strings $a$ and $b$ there exists a short program $p$ transforming $a$ to $b$ that has the least possible length and is simple conditional on $b$. In this paper we…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
The state complexity, respectively, nondeterministic state complexity of a regular language $L$ is the number of states of the minimal deterministic, respectively, of a minimal nondeterministic finite automaton for $L$. Some of the most…
We study the problem of automatically computing the time complexity of concurrent object-oriented programs. To determine this complexity we use intermediate abstract descriptions that record relevant information for the time analysis (cost…
We study the computational complexity theory of smooth, finite-dimensional dynamical systems. Building off of previous work, we give definitions for what it means for a smooth dynamical system to simulate a Turing machine. We then show that…