The content of the dissertation falls in the area of formal verification of probabilistic systems. It comprises four parts listed below: 1. the decision problem of (probabilistic) simulation preorder between probabilistic pushdown automata (pPDAs) and finite probabilistic automata (fPAs); 2. the decision problem of a bisimilarity metric on finite probabilistic automata (fPAs); 3. the approximat...

In this paper, we define the concept of probabilistic like Menger (probabilistic like quasi Menger) space (briefly, PLM-space (PLqM-space)). We present some coupled fixed point and fixed point results for certain contraction type maps in partially order PLM-spaces (PLqM- spaces).

Simple heuristics often show a remarkable performance in practice for optimization problems. Worst-case analysis falls short of explaining this performance. Because this, “beyond worst-case analysis” algorithms has recently gained lot attention, including probabilistic algorithms. The instances many problems are essentially discrete metric space. Probabilistic such nevertheless mostly been cond...

This paper considers the computational hardness of computing expected outcomes and deciding (universal) (positive) almost–sure termination of probabilistic programs. It is shown that computing lower and upper bounds of expected outcomes is Σ 1– and Σ 0 2–complete, respectively. Deciding (universal) almost–sure termination as well as deciding whether the expected outcome of a program equals a gi...

Three-valued Markov chains and their PCTL semantics abstract – via probabilistic simulations – labeled Markov chains and their usual PCTL semantics. This abstraction framework is complete for a PCTL formula if all labeled Markov chains that satisfy said formula have a finite-state abstraction that satisfies it in its abstract semantics. We show that not all PCTL formulae are complete for this a...

As probabilistic computations play an increasing role in solving various problems, researchers have designed probabilistic languages to facilitate their modeling. Most of the existing probabilistic languages, however, focus only on discrete distributions, and there has been little effort to develop probabilistic languages whose expressive power is beyond discrete distributions. This dissertatio...

Feature selection is a search problem for an \optimal" subset of features. The class separability is normally used as one of the basic feature selection criteria. Instead of maximizing the class separability as in the literature, this work adopts a criterion aiming to maintain the discriminating power of the data. After examining the pros and cons of two existing algorithms for feature selectio...

The main obstruction to automatic verification of concurrent systems is the hu e amount of memory required to complete the veriLation task (state explothis paper we present a probabilistic algorithm for automatic verification via model checking. Our algorithm trades space with time. In particular, when our memory is over because of state explosion our algorithm does not give up verijication. In...

We proposed a probabilistic algorithm to solve the Multiple Sequence Alignment problem. The algorithm is a Simulated Annealing (SA) that exploits the representation of the Multiple Alignment between D sequences as a directed polymer in D dimensions. Within this representation we can easily track the evolution in the configuration space of the alignment through local moves of low computational c...