We consider autoreducibility of complete sets for the two common types of probabilistic polynomial-time reductions: RP reductions containing one-sided errors on positive input instances only, and BPP reductions containing two-sided errors. Specifically, we focus on the probabilistic counterparts of the deterministic many-one and truthtable autoreductions. We prove that non-trivial complete sets...

We present a sound and complete axiomatization of finite complete trace semantics for generative probabilistic transition systems. Our approach is coalgebraic, which opens the door to axiomatize other types of systems. In order to prove soundness and completeness, we employ determinization and show that coalgebraic traces can be recovered via determinization, a result interesting in itself. The...

Probabilistic team semantics is a framework for logical analysis of probabilistic dependencies. Our focus on the axiomatizability, complexity, and expressivity inclusion logic its extensions. We identify natural fragment existential second-order with additive real arithmetic that captures exactly logic. furthermore relate these formalisms to linear programming, doing so obtain PTIME data comple...

We study the query evaluation problem in probabilistic databases in the presence of probabilistic existential rules. Our focus is on the Datalog± family of languages for which we define the probabilistic counterpart using a flexible and compact encoding of probabilities. This formalism can be viewed as a generalization of probabilistic databases, as it allows to generate new facts from the give...

in this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy nor...

in this paper, we formalize the menger probabilistic normed space as a category in which its objects are the menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. so, we can easily apply the results of topological vector spaces...

We consider a simple divergence-free language RP for reactive processes which includes prefixing, deterministic choice, actionguarded probabilistic choice, synchronous parallel and recursion. We show that the probabilistic bisimulation of Larsen & Skou is a congruence for this language. Following the methodology introduced by de Bakker & Zucker we give denotational semantics to this language by...

We deene probabilistic languages and probabilistic automata over a nite set of events. We also deene operators under which the set of probabilistic languages(p-languages) is closed, thus forming an algebra of p-languages. We show that this set is a complete partial order and our operators are continuous in it. Hence, recursive equations may be deened in this algebra using xpoints of continuous ...

We present properties of multihead two-way probabilistic nite automata that parallel those of their deterministic and nondeterministic counterparts. We deene multihead proba-bilistic nite automata with log-space constructible transition probabilities, and we describe a simple technique to simulate these automata by standard log-space probabilistic Turing machines. Next, we represent log-space p...

This thesis provides an algebraic modelling and verification of probabilistic concurrent systems in the style of Kleene algebra. Without concurrency, it is shown that the equational theory of continuous probabilistic Kleene algebra is complete with respect to an automata model under standard simulation equivalence. This yields a minimisation-based decision procedure for the algebra. Without pro...