Bisimilarity is not Borel

We prove that the relation of bisimilarity between countable labelled transition systems is $\Sigma_1^1$-complete (hence not Borel), by reducing the set of non-wellorders over the natural numbers continuously to it. This has an impact on the theory of probabilistic and nondeterministic processes over uncountable spaces, since logical characterizations of bisimilarity (as, for instance, those based on the unique structure theorem for analytic spaces) require a countable logic whose formulas have measurable semantics. Our reduction shows that such a logic does not exist in the case of image-infinite processes.Comment: 20 pages, 1 figure; proof of Sigma_1^1 completeness added with extended comments. I acknowledge careful reading by the referees. Major changes in Introduction, Conclusion, and motivation for NLMP. Proof for Lemma 22 added, simpler proofs for Lemma 17 and Theorem 30. Added references. Part of this work was presented at Dagstuhl Seminar 12411 on Coalgebraic Logic

Structural operational semantics for stochastic and weighted transition systems

We introduce weighted GSOS, a general syntactic framework to specify well-behaved transition systems where transitions are equipped with weights coming from a commutative monoid. We prove that weighted bisimilarity is a congruence on systems defined by weighted GSOS specifications. We illustrate the flexibility of the framework by instantiating it to handle some special cases, most notably that of stochastic transition systems. Through examples we provide weighted-GSOS definitions for common stochastic operators in the literature

LTLf and LDLf Monitoring: A Technical Report

Runtime monitoring is one of the central tasks to provide operational decision support to running business processes, and check on-the-fly whether they comply with constraints and rules. We study runtime monitoring of properties expressed in LTL on finite traces (LTLf) and in its extension LDLf. LDLf is a powerful logic that captures all monadic second order logic on finite traces, which is obtained by combining regular expressions and LTLf, adopting the syntax of propositional dynamic logic (PDL). Interestingly, in spite of its greater expressivity, LDLf has exactly the same computational complexity of LTLf. We show that LDLf is able to capture, in the logic itself, not only the constraints to be monitored, but also the de-facto standard RV-LTL monitors. This makes it possible to declaratively capture monitoring metaconstraints, and check them by relying on usual logical services instead of ad-hoc algorithms. This, in turn, enables to flexibly monitor constraints depending on the monitoring state of other constraints, e.g., "compensation" constraints that are only checked when others are detected to be violated. In addition, we devise a direct translation of LDLf formulas into nondeterministic automata, avoiding to detour to Buechi automata or alternating automata, and we use it to implement a monitoring plug-in for the PROM suite

Inductive Definition and Domain Theoretic Properties of Fully Abstract

A construction of fully abstract typed models for PCF and PCF^+ (i.e., PCF + "parallel conditional function"), respectively, is presented. It is based on general notions of sequential computational strategies and wittingly consistent non-deterministic strategies introduced by the author in the seventies. Although these notions of strategies are old, the definition of the fully abstract models is new, in that it is given level-by-level in the finite type hierarchy. To prove full abstraction and non-dcpo domain theoretic properties of these models, a theory of computational strategies is developed. This is also an alternative and, in a sense, an analogue to the later game strategy semantics approaches of Abramsky, Jagadeesan, and Malacaria; Hyland and Ong; and Nickau. In both cases of PCF and PCF^+ there are definable universal (surjective) functionals from numerical functions to any given type, respectively, which also makes each of these models unique up to isomorphism. Although such models are non-omega-complete and therefore not continuous in the traditional terminology, they are also proved to be sequentially complete (a weakened form of omega-completeness), "naturally" continuous (with respect to existing directed "pointwise", or "natural" lubs) and also "naturally" omega-algebraic and "naturally" bounded complete -- appropriate generalisation of the ordinary notions of domain theory to the case of non-dcpos.Comment: 50 page

The Complexity of Local Stratification

The class of locally stratified logic programs is shown to be Π11-complete by the construction of a reducibility of the class of infinitely branching nondeterministic finite register machines.nondeterministic finite register machines