Related papers: Bounds on the Automata Size for Presburger Arithme…
This paper studies explicit and theoretical bounds for several interesting quantities in number theory, conditionally on the Generalized Riemann Hypothesis. Specifically, we improve the existing explicit bounds for the least quadratic…
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.…
In this paper, we investigate the size of moments of quadratic character sums averaged over the family of fundamental discriminants. We obtain an asymptotic formula for all integer moments in a restricted range of parameters using a…
We make certain bounds in Krebs' proof of Cobham's theorem explicit and obtain corresponding upper bounds on the length of a common prefix of an aperiodic $a$-automatic sequence and an aperiodic $b$-automatic sequence, where $a$ and $b$ are…
In 1964 \v{C}ern\'{y} conjectured that each $n$-state synchronizing automaton posesses a reset word of length at most $(n-1)^2$. From the other side the best known upper bound on the reset length (minimum length of reset words) is cubic in…
We systematically study the boundaries of one-dimensional, 2-color cellular automata depending on 4 cells, begun from simple initial conditions. We determine the exact growth rates of the boundaries that appear to be reducible. Morphic…
Word equations are a crucial element in the theoretical foundation of constraint solving over strings, which have received a lot of attention in recent years. A word equation relates two words over string variables and constants. Its…
A complete deterministic finite (semi)automaton (DFA) with a set of states $Q$ is \emph{completely reachable} if every nonempty subset of $Q$ is the image of the action of some word applied to $Q$. The concept of completely reachable…
We provide new insights on the determinization and minimization of tree automata using congruences on trees. From this perspective, we study a Brzozowski's style minimization algorithm for tree automata. First, we prove correct this method…
This paper establishes a lower bound on the number of states necessary in the worst case to simulate an $n$-state two-way nondeterministic finite automaton (2NFA) by a one-way unambiguous finite automaton (UFA). It is proved that for every…
The emptiness and containment problems for probabilistic automata are natural quantitative generalisations of the classical language emptiness and inclusion problems for Boolean automata. It is well known that both problems are undecidable.…
It has been recently reported that classical systems have speed limit for state evolution, although such a concept of speed limit had been considered to be unique to quantum systems. Owing to the speed limit for classical system, the lower…
History-deterministic automata are those in which nondeterministic choices can be correctly resolved stepwise: there is a strategy to select a continuation of a run given the next input letter so that if the overall input word admits some…
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…
A $d$-limited automaton is a Turing machine that may rewrite each input cell at most~$d$ times. Hibbard (1967) showed that for every $d \geq 2$ such automata recognize all context-free languages and that deterministic $d$-limited automata…
We consider the state-minimisation problem for weighted and probabilistic automata. We provide a numerically stable polynomial-time minimisation algorithm for weighted automata, with guaranteed bounds on the numerical error when run with…
We present counting reward automata-a finite state machine variant capable of modelling any reward function expressible as a formal language. Unlike previous approaches, which are limited to the expression of tasks as regular languages, our…
One method to determine whether or not a system of partial differential equations is consistent is to attempt to construct a solution using merely the "algebraic data" associated to the system. In technical terms, this translates to the…
We present a description of rigid models of Presburger arithmetic (i.e., Z-groups). In particular, we show that Presburger arithmetic has rigid models of all infinite cardinalities up to the continuum, but no larger.
Presburger arithmetic is the first-order theory of the natural numbers with addition (but no multiplication). We characterize sets that can be defined by a Presburger formula as exactly the sets whose characteristic functions can be…