In this paper, we obtain closed formulas for the number of reachable vertices in labelled plane trees by paths lengths, sinks, leaf first children, left most path, non-first and non-leaves. Our counting objects are having their edges oriented from a vertex lower label towards higher label. For each statistic, average vertices. Moreover, formula on $n$ such that exactly $k\leq n$ root.

This paper establishes a relationship between reachability problems in timed automata and space-bounded counter automata. We show that reachability in timed automata with three or more clocks is naturally logarithmic-space interreducible with reachability in spacebounded counter automata with two counters. We moreover show the logarithmic-space equivalence of reachability in two-clock timed aut...

In this paper, we consider multi-dimensional maximal cost-bounded reachability probability over continuous-time Markov decision processes (CTMDPs). Our major contributions are as follows. Firstly, we derive an integral characterization which states that the maximal cost-bounded reachability probability function is the least fixed-point of a system of integral equations. Secondly, we prove that ...

This paper presents a disjointness analysis for Java-like languages. Two objects are disjoint if the parts of the heap reachable from the two objects are disjoint. The analysis is based on static reachability graphs, which characterize the reachability of each object in the heap from a set of objects of interest. Reachability graphs contain nodes to represent objects and edges to represent heap...

Reachability analysis is the most general approach to analyze Petri nets. Due to state space explosion , generation of the reachability set and reachability graph becomes intractable even for moderately sized nets with the known approaches. This paper presents a new method to generate and represent the reachability set and reachability graph of large Petri nets in a compositional and hierarchic...

Reachability analysis is the most general approach to analyze Petri nets. Due to state space explosion , generation of the reachability set and reachability graph becomes intractable even for moderately sized nets with the known approaches. This paper presents a new method to generate and represent the reachability set and reachability graph of large Petri nets in a compositional and hierarchic...