In this paper we develop an automata-theoretic framework for reasoning about infinite-state sequential systems. Our framework is based on the observation that states of such systems, which carry a finite but unbounded amount of information, can be viewed as nodes in an infinite tree, and transitions between states can be simulated by finite-state automata. Checking that a system satisfies a tem...

We examine the conjecture that no polynomial can upper bound the increase in the number of states when a one-way nondeterministic finite automaton (1nfa) is converted into an equivalent two-way deterministic finite automaton (2dfa). We study the problem of liveness, which admits 1nfas of polynomial size and is known to defy 2dfas of polynomial size if and only if the conjecture is true. We focu...

Consider a small group of mobile agents whose goal is to locate a certain cell in a two-dimensional infinite grid. The agents operate in an asynchronous environment, where in each discrete time step, an arbitrary subset of the agents execute one atomic look-compute-move cycle. The protocol controlling each agent is determined by a (possibly distinct) finite automaton. The only means of communic...

In theoretical computer science, the Turing machine has played a number of important roles in understanding and exploiting basic concepts and mechanisms in computing and information processing [20]. It is a simple mathematical model of computers [9]. After that, M.Blum and C.Hewitt first proposed two-dimensional automata as a computational model of two-dimensional pattern processing, and invest...

A theorem of Christol states that a power series over a finite field is algebraic over the polynomial ring if and only if its coefficients can be generated by a finite automaton. Using Christol’s result, we prove that the same assertion holds for generalized power series (whose index sets may be arbitrary well-ordered sets of nonnegative rationals).

multi agent markov decision processes (mmdps), as the generalization of markov decision processes to the multi agent case, have long been used for modeling multi agent system and are used as a suitable framework for multi agent reinforcement learning. in this paper, a generalized learning automata based algorithm for finding optimal policies in mmdp is proposed. in the proposed algorithm, mmdp ...

We represent a filamentous actin molecule as a graph of finite-state machines (F-actin automaton). Each node in the graph takes three states — resting, excited, refractory. All nodes update their states simultaneously and by the same rule, in discrete time steps. Two rules are considered: threshold rule — a resting node is excited if it has at least one excited neighbour and narrow excitation i...

In this paper we present ISA, an approach for learning and exploiting subgoals in episodic reinforcement (RL) tasks. ISA interleaves with the induction of a subgoal automaton, automaton whose edges are labeled by task’s expressed as propositional logic formulas over set high-level events. A also consists two special states: state indicating successful completion task, that task has finished wit...

Thermal noise in a cellular automaton refers to a random perturbation to its function which eventually leads this automaton to an equilibrium state controlled by a temperature parameter. We study the 1dimensional majority-3 cellular automaton under this model of noise. Without noise, each cell in this automaton decides its next state by majority voting among itself and its left and right neighb...

A complete deterministic finite automaton A is called synchronizing if the action of some word w resets A , that is, leaves the automaton in one particular state no matter at which state it is applied. Any such word w is said to be a reset word for the automaton. The minimum length of reset words for A is called the reset threshold of A and denoted by rt(A ). Synchronizing automata constitute a...