Pushdown automaton

About: Pushdown automaton is a research topic. Over the lifetime, 1868 publications have been published within this topic receiving 35399 citations.

Unambiguous auxiliary pushdown automata and semi-unbounded fan-in circuits

Abstract: Notions of unambiguity for uniform circuits and AuxPDA′s are studied and related to each other In particular, a coincidence for counting and unambiguous versions of AuxPDA′s and semi-unbounded fan-in circuits is shown Moreover, an improved simulation of LOGUCFL (the class of languages logspace many-one reducible to unambiguous context-free languages) by unambiguous circuits and AuxPDA′s is developed Next, an inductive counting technique on semi-unbounded fan-in circuits is presented and employed for several applications, especially an alternative proof for the closure under complementation of LOGCFL A cost-free simulation of polynomially ambiguity bounded AuxPDA′s by unambiguous ones is given A first nontrivial upper bound for a circuit class defined by Lange and its closure under complementation are indicated Finally, a normal form for AuxPDA′s is investigated Inter alia, it is shown that for unambiguous AuxPDA′s operating in polynomial time and logarithmic space a pushdown height of O(log2n) suffices, thus paralleling results for deterministic and nondeterministic AuxPDA′s It is pointed out that without loss of generality the underlying machines of the most important AuxPDA classes work obliviously

New Coins From Old: Computing With Unknown Bias

Abstract: Suppose that we are given a function f : (0, 1)→(0,1) and, for some unknown p∈(0, 1), a sequence of independent tosses of a p-coin (i.e., a coin with probability p of “heads”). For which functions f is it possible to simulate an f(p)-coin? This question was raised by S. Asmussen and J. Propp. A simple simulation scheme for the constant function f(p)≡1/2 was described by von Neumann (1951); this scheme can be easily implemented using a finite automaton. We prove that in general, an f(p)-coin can be simulated by a finite automaton for all p ∈ (0, 1), if and only if f is a rational function over ℚ. We also show that if an f(p)-coin can be simulated by a pushdown automaton, then f is an algebraic function over ℚ; however, pushdown automata can simulate f(p)-coins for certain nonrational functions such as $$f{\left( p \right)} = {\sqrt p }$$. These results complement the work of Keane and O’Brien (1994), who determined the functions f for which an f(p)-coin can be simulated when there are no computational restrictions on the simulation scheme.With an appendix by Christopher Hillar‡, University of California, Berkeley, 970 Evans Hall #3840, Berkeley, CA 94720-3840, USA, chillar@math.berkeley.edu

Decidability and Enumeration for Automatic Sequences: A Survey

Abstract: In this talk I will report on some recent results concerning decidability and enumeration for properties of automatic sequences. This is work with Jean-Paul Allouche, Emilie Charlier, Narad Rampersad, Dane Henshall, Luke Schaeffer, Eric Rowland, Daniel Goc, and Hamoon Mousavi.

Aspects of Reversibility for Classical Automata

Abstract: Some aspects of logical reversibility for computing devices with a finite number of discrete internal states are addressed. These devices have a read-only input tape, may be equipped with further resources, and evolve in discrete time. The reversibility of a computation means in essence that every configuration has a unique successor configuration and a unique predecessor configuration. The notion of reversibility is discussed. In which way is the predecessor configuration computed? May we use a universal device? Do we have to use a device of the same type? Or else a device with the same computational power? Do we have to consider all possible configurations as potential predecessors? Or only configurations that are reachable from some initial configurations? We present some selected aspects as gradual reversibility and time-symmetry as well as results on the computational capacity and decidability mainly of finite automata and pushdown automata, and draw attention to the overall picture and some of the main ideas involved.

The minimal cost reachability problem in priced timed pushdown systems

Abstract: This paper introduces the model of priced timed pushdown systems as an extension of discrete-timed pushdown systems with a cost model that assigns multidimensional costs to both transitions and stack symbols. For this model, we consider the minimal cost reachability problem: i.e., given a priced timed pushdown system and a target set of configurations, determine the minimal possible cost of any run from the initial to a target configuration. We solve the problem by reducing it to the reachability problem in standard pushdown systems.