Related papers: Probabilistic automatic complexity of finite strin…
We show that a well-known family of deterministic finite automata can be used to distinguish distinct binary strings of the same length from every start state. Further, we establish almost matching lower and upper bounds on the number of…
We consider finite two-way automata and measure the use of two-way motion by counting the number of left moves in accepting computations. Restriction of the automata according to this measure allows us to study in detail the use of two-way…
Constraints over finite sequences of variables are ubiquitous in sequencing and timetabling. Moreover, the wide variety of such constraints in practical applications led to general modelling techniques and generic propagation algorithms,…
The state complexity of the result of a regular operation is often positively correlated with the number of distinct transformations induced by letters in the minimal deterministic finite automaton of the input languages. That is, more…
State reduction of finite automata plays a significant role in improving efficiency in formal verification, pattern recognition, and machine learning, where automata-based models are widely used. While deterministic automata have…
Many graph algorithms can be viewed as sets of rules that are iteratively applied, with the number of iterations dependent on the size and complexity of the input graph. Existing machine learning architectures often struggle to represent…
This paper presents a new static analysis for deriving upper bounds on the expected resource consumption of probabilistic programs. The analysis is fully automatic and derives symbolic bounds that are multivariate polynomials of the inputs.…
We introduce Merlin-Arthur (MA) automata where Merlin provides a certificate at the beginning of computation and it is scanned by Arthur before reading the input. We define Merlin-Arthur deterministic, probabilistic, and quantum finite…
We obtain an index of the complexity of a random sequence by allowing the role of the measure in classical probability theory to be played by a function we call the generating mechanism. Typically, this generating mechanism will be a finite…
In this paper the stochastic complexity criterion is applied to estimation of the order in AR and ARMA models. The power of the criterion for short strings is illustrated by simulations. It requires an integral of the square root of Fisher…
The paper provides results regarding the computational complexity of hybrid system identification. More precisely, we focus on the estimation of piecewise affine (PWA) maps from input-output data and analyze the complexity of computing a…
Affine automata provide a finite-state computational model that preserves the linear-algebraic structure of quantum computation while operating entirely over the reals. Recent work has shown that affine automata can far surpass classical…
In this paper, a compressed membership problem for finite automata, both deterministic and non-deterministic, with compressed transition labels is studied. The compression is represented by straight-line programs (SLPs), i.e. context-free…
There are many evaluation strategies for term rewrite systems, but automatically proving termination or analyzing complexity is usually easiest for innermost rewriting. Several syntactic criteria exist when innermost termination implies…
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…
Generalizing the notion of automatic complexity of individual strings due to Shallit and Wang, we define the automatic complexity $A(E)$ of an equivalence relation $E$ on a finite set $S$ of strings. We prove that the problem of determining…
We use results from communication complexity, both new and old ones, to prove lower bounds for unambiguous finite automata (UFAs). We show three results. $\textit{Complement:}$ There is a language $L$ recognised by an $n$-state UFA such…
We discuss the problem of learning a deterministic finite automaton (DFA) from a confidence oracle. That is, we are given access to an oracle $Q$ with incomplete knowledge of some target language $L$ over an alphabet $\Sigma$; the oracle…
Descriptional complexity is the study of the conciseness of the various models representing formal languages. The state complexity of a regular language is the size, measured by the number of states of the smallest, either deterministic or…
In this paper, we study the approximate minimization problem of weighted finite automata (WFAs): to compute the best possible approximation of a WFA given a bound on the number of states. By reformulating the problem in terms of Hankel…