768 research outputs found
Mean-payoff Automaton Expressions
Quantitative languages are an extension of boolean languages that assign to
each word a real number. Mean-payoff automata are finite automata with
numerical weights on transitions that assign to each infinite path the long-run
average of the transition weights. When the mode of branching of the automaton
is deterministic, nondeterministic, or alternating, the corresponding class of
quantitative languages is not robust as it is not closed under the pointwise
operations of max, min, sum, and numerical complement. Nondeterministic and
alternating mean-payoff automata are not decidable either, as the quantitative
generalization of the problems of universality and language inclusion is
undecidable.
We introduce a new class of quantitative languages, defined by mean-payoff
automaton expressions, which is robust and decidable: it is closed under the
four pointwise operations, and we show that all decision problems are decidable
for this class. Mean-payoff automaton expressions subsume deterministic
mean-payoff automata, and we show that they have expressive power incomparable
to nondeterministic and alternating mean-payoff automata. We also present for
the first time an algorithm to compute distance between two quantitative
languages, and in our case the quantitative languages are given as mean-payoff
automaton expressions
Spatial patterns and scale freedom in a Prisoner's Dilemma cellular automata with Pavlovian strategies
A cellular automaton in which cells represent agents playing the Prisoner's
Dilemma (PD) game following the simple "win-stay, loose-shift" strategy is
studied. Individuals with binary behavior, such as they can either cooperate
(C) or defect (D), play repeatedly with their neighbors (Von Neumann's and
Moore's neighborhoods). Their utilities in each round of the game are given by
a rescaled payoff matrix described by a single parameter Tau, which measures
the ratio of 'temptation to defect' to 'reward for cooperation'. Depending on
the region of the parameter space Tau, the system self-organizes - after a
transient - into dynamical equilibrium states characterized by different
definite fractions of C agents (2 states for the Von Neumann neighborhood and 4
for Moore neighborhood). For some ranges of Tau the cluster size distributions,
the power spectrums P(f) and the perimeter-area curves follow power-law
scalings. Percolation below threshold is also found for D agent clusters. We
also analyze the asynchronous dynamics version of this model and compare
results.Comment: Accepted for publication in JSTA
Comparator automata in quantitative verification
The notion of comparison between system runs is fundamental in formal
verification. This concept is implicitly present in the verification of
qualitative systems, and is more pronounced in the verification of quantitative
systems. In this work, we identify a novel mode of comparison in quantitative
systems: the online comparison of the aggregate values of two sequences of
quantitative weights. This notion is embodied by {\em comparator automata}
({\em comparators}, in short), a new class of automata that read two infinite
sequences of weights synchronously and relate their aggregate values.
We show that {aggregate functions} that can be represented with B\"uchi
automaton result in comparators that are finite-state and accept by the B\"uchi
condition as well. Such {\em -regular comparators} further lead to
generic algorithms for a number of well-studied problems, including the
quantitative inclusion and winning strategies in quantitative graph games with
incomplete information, as well as related non-decision problems, such as
obtaining a finite representation of all counterexamples in the quantitative
inclusion problem.
We study comparators for two aggregate functions: discounted-sum and
limit-average. We prove that the discounted-sum comparator is -regular
iff the discount-factor is an integer. Not every aggregate function, however,
has an -regular comparator. Specifically, we show that the language of
sequence-pairs for which limit-average aggregates exist is neither
-regular nor -context-free. Given this result, we introduce the
notion of {\em prefix-average} as a relaxation of limit-average aggregation,
and show that it admits -context-free comparators
On the Role of External Constraints in a Spatially Extended Evolutionary Prisoner's Dilemma Game
We study the emergency of mutual cooperation in evolutionary prisoner's
dilemma games when the players are located on a square lattice. The players can
choose one of the three strategies: cooperation (C), defection (D) or "tit for
tat" (T), and their total payoffs come from games with the nearest neighbors.
During the random sequential updates the players adopt one of their neighboring
strategies if the chosen neighbor has higher payoff. We compare the effect of
two types of external constraints added to the Darwinian evolutionary
processes. In both cases the strategy of a randomly chosen player is replaced
with probability P by another strategy. In the first case, the strategy is
replaced by a randomly chosen one among the two others, while in the second
case the new strategy is always C. Using generalized mean-field approximations
and Monte Carlo simulations the strategy concentrations are evaluated in the
stationary state for different strength of external constraints characterized
by the probability P.Comment: 19 pages, 10 figure
Analysis of reinforcement learning strategies for predation in a mimic-model prey environment
In this paper we propose a mathematical learning model for a stochastic automaton simulating the
behaviour of a predator operating in a random environment occupied by two types of prey:
palatable mimics and unpalatable models. Specifically, a well known linear reinforcement learning
algorithm is used to update the probabilities of the two actions, eat prey or ignore prey, at every
random encounter. Each action elicits a probabilistic response from the environment that can be
either favorable or unfavourable. We analyse both fixed and varying stochastic responses for the
system. The basic approach of mimicry is defined and a short review of relevant previous approaches in
the literature is given. Finally, the conditions for continuous predator performance improvement are
explicitly formulated and precise definitions of predatory efficiency and mimicry efficiency are
also provided
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