Pushdown automaton

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

Algorithmic Meta Theorems for Circuit Classes of Constant and Logarithmic Depth.

Abstract: An algorithmic meta theorem for a logic and a class C of structures states that all problems expressible in this logic can be solved eciently for inputs from C. The prime example is Courcelle’s Theorem, which states that monadic second-order (mso) definable problems are linear-time solvable on graphs of bounded tree width. We contribute new algorithmic meta theorems, which state that mso-definable problems are (a) solvable by uniform constant-depth circuit families (AC 0 for decision problems and TC 0 for counting problems) when restricted to input structures of bounded tree depth and (b) solvable by uniform logarithmic-depth circuit families (NC 1 for decision problems and #NC 1 for counting problems) when a tree decomposition of bounded width in term representation is part of the input. Applications of our theorems include a TC 0 -completeness proof for the unary version of integer linear programming with a fixed number of equations and extensions of a recent result that counting the number of accepting paths of a visible pushdown automaton lies in #NC 1 . Our main technical contributions are a new tree automata model for unordered, unranked, labeled trees; a method for representing the tree automata’s computations algebraically using convolution circuits; and a lemma on computing balanced width-3 tree decompositions of trees in TC 0 , which encapsulates most of the technical diculties surrounding earlier results connecting tree automata and NC 1 . 1998 ACM Subject Classification F.1.3 Complexity Measures and Classes

Magic Numbers and Ternary Alphabet

Abstract: A number ?, in the range from n to 2 n , is magic for n with respect to a given alphabet size s, if there is no minimal nondeterministic finite automaton of n states and s input letters whose equivalent minimal deterministic finite automaton has ? states. We show that in the case of a ternary alphabet, there are no magic numbers. For all n and ? satisfying that $n \leqslant \alpha \leqslant 2^n$, we describe an n-state nondeterministic automaton with a three-letter input alphabet that needs ? deterministic states.

Reasoning about Recursive Probabilistic Programs

Abstract: This paper presents a wp-style calculus for obtaining expectations on the outcomes of (mutually) recursive probabilistic programs. We provide several proof rules to derive one-- and two--sided bounds for such expectations, and show the soundness of our wp-calculus with respect to a probabilistic pushdown automaton semantics. We also give a wp-style calculus for obtaining bounds on the expected runtime of recursive programs that can be used to determine the (possibly infinite) time until termination of such programs.

Descriptional complexity of bounded context-free languages

Abstract: Finite-turn pushdown automata (PDA) are investigated concerning their descriptional complexity. It is known that they accept exactly the class of ultralinear context-free languages. Furthermore, the increase in size when converting arbitrary PDAs accepting ultralinear languages to finite-turn PDAs cannot be bounded by any recursive function. The latter phenomenon is known as non-recursive trade-off. In this paper, finite-turn PDAs accepting letter-bounded languages are considered. It turns out that in this case the non-recursive trade-off is reduced to a recursive trade-off, more precisely, to an exponential trade-off. A conversion algorithm is presented and the optimality of the construction is shown by proving tight lower bounds. Furthermore, the question of reducing the number of turns of a given finite-turn PDA is studied. Again, a conversion algorithm is provided which shows that in this case the trade-off is at most polynomial.

AalWiNes: a fast and quantitative what-if analysis tool for MPLS networks

Abstract: We present an automated what-if analysis tool AalWiNes for MPLS networks which allows us to verify both logical properties (e.g., related to the policy compliance) as well as quantitative properties (e.g., concerning the latency) under multiple link failures. Our tool relies on weighted pushdown automata, a quantitative extension of classic automata theory, and takes into account the actual dataplane configuration, rendering it especially useful for debugging. In particular, our tool collects the different router forwarding tables and then builds a pushdown system, on which quantitative reachability is performed based on an expressive query language. Our experiments show that our tool outperforms state-of-the-art approaches (which until now have been restricted to logical properties) by several orders of magnitude; furthermore, our quantitative extension only entails a moderate overhead in terms of runtime. The tool comes with a platform-independent user interface and is publicly available as open-source, together with all other experimental artefacts.