7,789 research outputs found
Higher-Order Matching, Games and Automata
Higher-order matching is the problem given t = u where t, u are terms of simply typed Ν-calculus and u is closed, is there a substitution θ such that tθ and u have the same normal form with respect to βΡ-equality: can t be pattern matched to u? This paper considers the question: can we characterize the set of all solution terms to a matching problem? We provide an automata-theoretic account that is relative to resource: given a matching problem and a finite set of variables and constants, the (possibly infinite) set of terms that are built from those components and that solve the problem is regular. The characterization uses standard bottom-up tree automata. 1
Visibly Linear Dynamic Logic
We introduce Visibly Linear Dynamic Logic (VLDL), which extends Linear
Temporal Logic (LTL) by temporal operators that are guarded by visibly pushdown
languages over finite words. In VLDL one can, e.g., express that a function
resets a variable to its original value after its execution, even in the
presence of an unbounded number of intermediate recursive calls. We prove that
VLDL describes exactly the -visibly pushdown languages. Thus it is
strictly more expressive than LTL and able to express recursive properties of
programs with unbounded call stacks.
The main technical contribution of this work is a translation of VLDL into
-visibly pushdown automata of exponential size via one-way alternating
jumping automata. This translation yields exponential-time algorithms for
satisfiability, validity, and model checking. We also show that visibly
pushdown games with VLDL winning conditions are solvable in triply-exponential
time. We prove all these problems to be complete for their respective
complexity classes.Comment: 25 Page
Leaving the prison: A discussion of the Iterated prisoner`s dilemma under preferential partner selection.
Outside prison agents do not only ehoose a game strategy but also a game partner. In this paper players are finite automata and willing to interaet only if their expected payoff exeeeds an endogenously evolving aeeeptable minimum. In the resulting behavioural strueture the initial population is subdivided aeeording to players' degree of exploitiveness. If the number of eooperators is at least two, eooperators will be better off than defeetors. If more sueeessful automata reproduce, simulations show that due to partner seleetion eooperative behaviour is irnmune to invading mutants even if the life-span of generations is short.Prisoner`s dilemma; Partner selection; Finite automata; Matching;
Fashion, Cooperation, and Social Interactions
Fashion plays such a crucial rule in the evolution of culture and society
that it is regarded as a second nature to the human being. Also, its impact on
economy is quite nontrivial. On what is fashionable, interestingly, there are
two viewpoints that are both extremely widespread but almost opposite:
conformists think that what is popular is fashionable, while rebels believe
that being different is the essence. Fashion color is fashionable in the first
sense, and Lady Gaga in the second. We investigate a model where the population
consists of the afore-mentioned two groups of people that are located on social
networks (a spatial cellular automata network and small-world networks). This
model captures two fundamental kinds of social interactions (coordination and
anti-coordination) simultaneously, and also has its own interest to game
theory: it is a hybrid model of pure competition and pure cooperation. This is
true because when a conformist meets a rebel, they play the zero sum matching
pennies game, which is pure competition. When two conformists (rebels) meet,
they play the (anti-) coordination game, which is pure cooperation. Simulation
shows that simple social interactions greatly promote cooperation: in most
cases people can reach an extraordinarily high level of cooperation, through a
selfish, myopic, naive, and local interacting dynamic (the best response
dynamic). We find that degree of synchronization also plays a critical role,
but mostly on the negative side. Four indices, namely cooperation degree,
average satisfaction degree, equilibrium ratio and complete ratio, are defined
and applied to measure people's cooperation levels from various angles. Phase
transition, as well as emergence of many interesting geographic patterns in the
cellular automata network, is also observed.Comment: 21 pages, 12 figure
Buffered Simulation Games for B\"uchi Automata
Simulation relations are an important tool in automata theory because they
provide efficiently computable approximations to language inclusion. In recent
years, extensions of ordinary simulations have been studied, for instance
multi-pebble and multi-letter simulations which yield better approximations and
are still polynomial-time computable.
In this paper we study the limitations of approximating language inclusion in
this way: we introduce a natural extension of multi-letter simulations called
buffered simulations. They are based on a simulation game in which the two
players share a FIFO buffer of unbounded size. We consider two variants of
these buffered games called continuous and look-ahead simulation which differ
in how elements can be removed from the FIFO buffer. We show that look-ahead
simulation, the simpler one, is already PSPACE-hard, i.e. computationally as
hard as language inclusion itself. Continuous simulation is even EXPTIME-hard.
We also provide matching upper bounds for solving these games with infinite
state spaces.Comment: In Proceedings AFL 2014, arXiv:1405.527
Infinite games with finite knowledge gaps
Infinite games where several players seek to coordinate under imperfect
information are deemed to be undecidable, unless the information is
hierarchically ordered among the players.
We identify a class of games for which joint winning strategies can be
constructed effectively without restricting the direction of information flow.
Instead, our condition requires that the players attain common knowledge about
the actual state of the game over and over again along every play.
We show that it is decidable whether a given game satisfies the condition,
and prove tight complexity bounds for the strategy synthesis problem under
-regular winning conditions given by parity automata.Comment: 39 pages; 2nd revision; submitted to Information and Computatio
Cooperative Strategies in Groups of Strangers: An Experiment
We study cooperation in four-person economies of indefinite duration. Subjects interact anonymously playing a prisonerâs dilemma. We identify and characterize the strategies employed at the aggregate and at the individual level. We find that (i) grim trigger well describes aggregate play, but not individual play; (ii) individual behavior is persistently heterogeneous; (iii) coordination on cooperative strategies does not improve with experience; (iv) systematic defection does not crowd-out systematic cooperation.repeated games, equilibrium selection, prisonersâ dilemma, random matching
Decision Problems for Deterministic Pushdown Automata on Infinite Words
The article surveys some decidability results for DPDAs on infinite words
(omega-DPDA). We summarize some recent results on the decidability of the
regularity and the equivalence problem for the class of weak omega-DPDAs.
Furthermore, we present some new results on the parity index problem for
omega-DPDAs. For the specification of a parity condition, the states of the
omega-DPDA are assigned priorities (natural numbers), and a run is accepting if
the highest priority that appears infinitely often during a run is even. The
basic simplification question asks whether one can determine the minimal number
of priorities that are needed to accept the language of a given omega-DPDA. We
provide some decidability results on variations of this question for some
classes of omega-DPDAs.Comment: In Proceedings AFL 2014, arXiv:1405.527
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