5,267 research outputs found
Well structured program equivalence is highly undecidable
We show that strict deterministic propositional dynamic logic with
intersection is highly undecidable, solving a problem in the Stanford
Encyclopedia of Philosophy. In fact we show something quite a bit stronger. We
introduce the construction of program equivalence, which returns the value
precisely when two given programs are equivalent on halting
computations. We show that virtually any variant of propositional dynamic logic
has -hard validity problem if it can express even just the equivalence
of well-structured programs with the empty program \texttt{skip}. We also show,
in these cases, that the set of propositional statements valid over finite
models is not recursively enumerable, so there is not even an axiomatisation
for finitely valid propositions.Comment: 8 page
Real-time and Probabilistic Temporal Logics: An Overview
Over the last two decades, there has been an extensive study on logical
formalisms for specifying and verifying real-time systems. Temporal logics have
been an important research subject within this direction. Although numerous
logics have been introduced for the formal specification of real-time and
complex systems, an up to date comprehensive analysis of these logics does not
exist in the literature. In this paper we analyse real-time and probabilistic
temporal logics which have been widely used in this field. We extrapolate the
notions of decidability, axiomatizability, expressiveness, model checking, etc.
for each logic analysed. We also provide a comparison of features of the
temporal logics discussed
Bayesian Logic Programs
Bayesian networks provide an elegant formalism for representing and reasoning
about uncertainty using probability theory. Theyare a probabilistic extension
of propositional logic and, hence, inherit some of the limitations of
propositional logic, such as the difficulties to represent objects and
relations. We introduce a generalization of Bayesian networks, called Bayesian
logic programs, to overcome these limitations. In order to represent objects
and relations it combines Bayesian networks with definite clause logic by
establishing a one-to-one mapping between ground atoms and random variables. We
show that Bayesian logic programs combine the advantages of both definite
clause logic and Bayesian networks. This includes the separation of
quantitative and qualitative aspects of the model. Furthermore, Bayesian logic
programs generalize both Bayesian networks as well as logic programs. So, many
ideas developedComment: 52 page
Probabilistic Programming Concepts
A multitude of different probabilistic programming languages exists today,
all extending a traditional programming language with primitives to support
modeling of complex, structured probability distributions. Each of these
languages employs its own probabilistic primitives, and comes with a particular
syntax, semantics and inference procedure. This makes it hard to understand the
underlying programming concepts and appreciate the differences between the
different languages. To obtain a better understanding of probabilistic
programming, we identify a number of core programming concepts underlying the
primitives used by various probabilistic languages, discuss the execution
mechanisms that they require and use these to position state-of-the-art
probabilistic languages and their implementation. While doing so, we focus on
probabilistic extensions of logic programming languages such as Prolog, which
have been developed since more than 20 years
Applying Formal Methods to Networking: Theory, Techniques and Applications
Despite its great importance, modern network infrastructure is remarkable for
the lack of rigor in its engineering. The Internet which began as a research
experiment was never designed to handle the users and applications it hosts
today. The lack of formalization of the Internet architecture meant limited
abstractions and modularity, especially for the control and management planes,
thus requiring for every new need a new protocol built from scratch. This led
to an unwieldy ossified Internet architecture resistant to any attempts at
formal verification, and an Internet culture where expediency and pragmatism
are favored over formal correctness. Fortunately, recent work in the space of
clean slate Internet design---especially, the software defined networking (SDN)
paradigm---offers the Internet community another chance to develop the right
kind of architecture and abstractions. This has also led to a great resurgence
in interest of applying formal methods to specification, verification, and
synthesis of networking protocols and applications. In this paper, we present a
self-contained tutorial of the formidable amount of work that has been done in
formal methods, and present a survey of its applications to networking.Comment: 30 pages, submitted to IEEE Communications Surveys and Tutorial
A Logic Programming Approach to Knowledge-State Planning: Semantics and Complexity
We propose a new declarative planning language, called K, which is based on
principles and methods of logic programming. In this language, transitions
between states of knowledge can be described, rather than transitions between
completely described states of the world, which makes the language well-suited
for planning under incomplete knowledge. Furthermore, it enables the use of
default principles in the planning process by supporting negation as failure.
Nonetheless, K also supports the representation of transitions between states
of the world (i.e., states of complete knowledge) as a special case, which
shows that the language is very flexible. As we demonstrate on particular
examples, the use of knowledge states may allow for a natural and compact
problem representation. We then provide a thorough analysis of the
computational complexity of K, and consider different planning problems,
including standard planning and secure planning (also known as conformant
planning) problems. We show that these problems have different complexities
under various restrictions, ranging from NP to NEXPTIME in the propositional
case. Our results form the theoretical basis for the DLV^K system, which
implements the language K on top of the DLV logic programming system.Comment: 48 pages, appeared as a Technical Report at KBS of the Vienna
University of Technology, see http://www.kr.tuwien.ac.at/research/reports
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