533 research outputs found
Bounded nondeterminism and the approximation induction principle in process algebra (extended abstract)
This paper presents a new semantics of ACPτ, the Algebra of Communicating Processes with abstraction. This leads to a term model of ACPτ which is isomorphic to the model of process graphs modulo rooted τδ-bisimulation of Baeten, Bergstra & Klop In this model, the Recursive Definition Principle (RDP), the Commutativity of Abstraction (CA) and Koomen's Fair Abstraction Rule (KFAR) are satisfied, but the Approximation Induction Principle (AIP) is not. The combination of these four principles is proven to be inconsistent, while any combination of three of them is not. In [2] a restricted version of AIP is proved valid in the graph model. This paper proposes a simpler and less restrictive version of AIP, not containing guarded recursive specifications as a parameter, which is still valid. This infinitary rule is formulated with the help of a family Bn of unary predicates, expressing bounded nondeterminism
Modal Logic and the Approximation Induction Principle
We prove a compactness theorem in the context of Hennessy-Milner logic. It is
used to derive a sufficient condition on modal characterizations for the
Approximation Induction Principle to be sound modulo the corresponding process
equivalence. We show that this condition is necessary when the equivalence in
question is compositional with respect to the projection operators
Another look at abstraction in process algebra
Central to theories of concurrency is the notion of abstraction. Abstraction from internal actions is the most important tool for system verification. In this paper, we look at abstraction in the framework of the Algebra of Communicating Processes (see BERGSTRA & KLOP [4, 6]). We introduce a hidden step η, and construct a model for the resulting theory ACPη. We briefly look at recursive specifications in this theory, and discuss the relations with Milner's silent step τ
A Denotational Semantics for First-Order Logic
In Apt and Bezem [AB99] (see cs.LO/9811017) we provided a computational
interpretation of first-order formulas over arbitrary interpretations. Here we
complement this work by introducing a denotational semantics for first-order
logic. Additionally, by allowing an assignment of a non-ground term to a
variable we introduce in this framework logical variables.
The semantics combines a number of well-known ideas from the areas of
semantics of imperative programming languages and logic programming. In the
resulting computational view conjunction corresponds to sequential composition,
disjunction to ``don't know'' nondeterminism, existential quantification to
declaration of a local variable, and negation to the ``negation as finite
failure'' rule. The soundness result shows correctness of the semantics with
respect to the notion of truth. The proof resembles in some aspects the proof
of the soundness of the SLDNF-resolution.Comment: 17 pages. Invited talk at the Computational Logic Conference (CL
2000). To appear in Springer-Verlag Lecture Notes in Computer Scienc
Stochastic Invariants for Probabilistic Termination
Termination is one of the basic liveness properties, and we study the
termination problem for probabilistic programs with real-valued variables.
Previous works focused on the qualitative problem that asks whether an input
program terminates with probability~1 (almost-sure termination). A powerful
approach for this qualitative problem is the notion of ranking supermartingales
with respect to a given set of invariants. The quantitative problem
(probabilistic termination) asks for bounds on the termination probability. A
fundamental and conceptual drawback of the existing approaches to address
probabilistic termination is that even though the supermartingales consider the
probabilistic behavior of the programs, the invariants are obtained completely
ignoring the probabilistic aspect.
In this work we address the probabilistic termination problem for
linear-arithmetic probabilistic programs with nondeterminism. We define the
notion of {\em stochastic invariants}, which are constraints along with a
probability bound that the constraints hold. We introduce a concept of {\em
repulsing supermartingales}. First, we show that repulsing supermartingales can
be used to obtain bounds on the probability of the stochastic invariants.
Second, we show the effectiveness of repulsing supermartingales in the
following three ways: (1)~With a combination of ranking and repulsing
supermartingales we can compute lower bounds on the probability of termination;
(2)~repulsing supermartingales provide witnesses for refutation of almost-sure
termination; and (3)~with a combination of ranking and repulsing
supermartingales we can establish persistence properties of probabilistic
programs.
We also present results on related computational problems and an experimental
evaluation of our approach on academic examples.Comment: Full version of a paper published at POPL 2017. 20 page
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