Pushdown automaton

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

Bisimilarity of Probabilistic Pushdown Automata

Abstract: We study the bisimilarity problem for probabilistic pushdown automata (pPDA) and subclasses thereof. Our definition of pPDA allows both probabilistic and non-deterministic branching, generalising the classical notion of pushdown automata (without epsilon-transitions). Our first contribution is a general construction that reduces checking bisimilarity of probabilistic transition systems to checking bisimilarity of non-deterministic transition systems. This construction directly yields decidability of bisimilarity for pPDA, as well as an elementary upper bound for the bisimilarity problem on the subclass of probabilistic basic process algebras, i.e., single-state pPDA. We further show that, with careful analysis, the general reduction can be used to prove an EXPTIME upper bound for bisimilarity of probabilistic visibly pushdown automata. Here we also provide a matching lower bound, establishing EXPTIME-completeness. Finally we prove that deciding bisimilarity of probabilistic one-counter automata, another subclass of pPDA, is PSPACE-complete. Here we use a more specialised argument to obtain optimal complexity bounds.

Reachability in recursive markov decision processes

Abstract: We consider a class of infinite-state Markov decision processes generated by stateless pushdown automata. This class corresponds to $1 \frac{1}{2}$-player games over graphs generated by BPA systems or (equivalently) 1-exit recursive state machines. An extended reachability objective is specified by two sets S and T of safe and terminal stack configurations, where the membership to S and T depends just on the top-of-the-stack symbol. The question is whether there is a suitable strategy such that the probability of hitting a terminal configuration by a path leading only through safe configurations is equal to (or different from) a given x ∈{0,1}. We show that the qualitative extended reachability problem is decidable in polynomial time, and that the set of all configurations for which there is a winning strategy is effectively regular. More precisely, this set can be represented by a deterministic finite-state automaton with a fixed number of control states. This result is a generalization of a recent theorem by Etessami & Yannakakis which says that the qualitative termination for 1-exit RMDPs (which exactly correspond to our $1 \frac{1}{2}$-player BPA games) is decidable in polynomial time. Interestingly, the properties of winning strategies for the extended reachability objectives are quite different from the ones for termination, and new observations are needed to obtain the result. As an application, we derive the EXPTIME-completeness of the model-checking problem for $1 \frac{1}{2}$-player BPA games and qualitative PCTL formulae.

Some aspects of linear space automata

Abstract: Linear space automaton is introduced as a generalization of probabilistic automaton and its various properties are investigated Linear space automaton has the abilities equivalent to probabilistic automaton but we can treat the former more easily than the latter because we can make use of properties of the linear space, successfully First the solutions are given for the problems of connectivity, state equivalence, reduction and identification of linear space automata Second, the matrix representation of linear space automaton is investigated and the relations between linear space automaton and probabilistic automaton are shown Third, we discuss the closure properties of the family of all real functions on a free semigroup Σ* which are defined by linear space automata and then give a solution to the synthesis problem of linear space automata Finally, some considerations are given to the problems of sets of tapes accepted by la's and also of operations under which the family of all the output functions of la's is not closed

Extended Two-Way Ordered Restarting Automata for Picture Languages

Abstract: We introduce a two-dimensional variant of the deterministic restarting automaton for processing rectangular pictures. Our device has a window of size three-by-three, in a rewrite step it can only replace the symbol in the central position of its window by a symbol that is smaller with respect to a fixed ordering on the tape alphabet, and it can only perform extended move-right and move-down steps. This automaton is strictly more expressive than the deterministic Sgraffito automaton, but its word problem can still be solved in polynomial time, and when restricted to one-dimensional input, it only accepts the regular languages.

On the descriptional power of heads, counters, and pebbles

Abstract: We investigate the descriptional complexity of deterministic two-way k-head finite automata (k- DHA). It is shown that between non-deterministic pushdown automata and any k-DHA, k ≥ 2, there are savings in the size of description which cannot be bounded by any recursive function. The same is true for the other end of the hierarchy. Such non-recursive trade-offs are also shown between any k-DHA, k ≥ 1, and DSPACE(log) = multi-DHA. We also address the particular case of unary languages. In general, it is possible that non-recursive trade-offs for arbitrary languages reduce to recursive trade-offs for unary languages. Here we present huge lower bounds for the unary trade-offs between non-deterministic finite automata and any k-DHA, k ≥ 2. Furthermore, several known simulation results imply the presented trade-offs for other descriptional systems, e.g., deterministic two-way finite automata with k pebbles or with k linearly bounded counters.