Related papers: New tools for state complexity
Counter automata are more powerful versions of finite-state automata where addition and subtraction operations are permitted on a set of n integer registers, called counters. We show that the word problem of $\Z^n$ is accepted by a…
Most slowly synchronizing automata over binary alphabets are circular, i.e., containing a letter permuting the states in a single cycle, and their set of synchronizing words has maximal state complexity, which also implies complete…
Fuelled by the popularity of the transformer architecture in deep learning, several works have investigated what formal languages a transformer can learn from data. Nonetheless, existing results remain hard to compare due to methodological…
Computational mechanics, an approach to structural complexity, defines a process's causal states and gives a procedure for finding them. We show that the causal-state representation--an $\epsilon$-machine--is the minimal one consistent with…
We investigate the nondeterministic state complexity of basic operations for suffix-free regular languages. The nondeterministic state complexity of an operation is the number of states that are necessary and sufficient in the worst-case…
Although algorithm is one of the central subjects, there have been little common understandings of what an algorithm is. For example, Gurevich view algorithms as abstract state machines, while others view algorithms as recursors. We promote…
In terms of the concepts of state and state transition, a new heuristic random search algorithm named state transition algorithm is proposed. For continuous function optimization problems, four special transformation operators called…
A sequence function alternative representation of state machines.
A turn in a computation of a pushdown automaton is a switch from a phase in which the height of the pushdown store increases to a phase in which it decreases. Given a pushdown or one-counter automaton, we consider, for each string in its…
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…
The quotient complexity, also known as state complexity, of a regular language is the number of distinct left quotients of the language. The quotient complexity of an operation is the maximal quotient complexity of the language resulting…
The projected language of a general deterministic automaton with $n$ states is recognizable by a deterministic automaton with $2^{n-1} + 2^{n-m} - 1$ states, where $m$ denotes the number of states incident to unobservable non-loop…
Automaton models are often seen as interpretable models. Interpretability itself is not well defined: it remains unclear what interpretability means without first explicitly specifying objectives or desired attributes. In this paper, we…
Let us consider an infinite word and $k\geq 1$ an integer. By steps of $k$, we substitute a letter ofthis infinite word by the power of an external letter. The new word obtaining by this process is called $k$ to $k$ substitution of a power…
A metamorphic robotic system is an aggregate of homogeneous robot units which can individually and selectively locomote in such a way as to change the global shape of the system. We introduce a mathematical framework for defining and…
The Fibonacci infinite word ${\bf f} = (f_i)_{i \geq 0} = 01001010\cdots$ is one of the most celebrated objects in combinatorics on words. There is a simple $5$-state automaton that, given $i$ in lsd-first Zeckendorf representation,…
We define the algorithmic complexity of a quantum state relative to a given precision parameter, and give upper bounds for various examples of states. We also establish a connection between the entanglement of a quantum state and its…
This paper investigates the state complexities of subword-closed and superword-closed languages, comparing them to regular languages. We focus on the square root operator and the substitution operator. We establish an exponential lower…
We introduce homing vector automata, which are finite automata augmented by a vector that is multiplied at each step by a matrix determined by the current transition, and have to return the vector to its original setting in order to accept…
Recent analysis of classical algorithms resulted in their axiomatization as transition systems satisfying some simple postulates, and in the formulation of the Abstract State Machine Theorem, which assures us that any classical algorithm…