359 research outputs found
Fee-Setting Mechanisms: On Optimal Pricing by Intermediaries and Indirect Taxation
Mechanisms according to which private intermediaries or governments charge
transaction fees or indirect taxes are prevalent in practice. We consider a setup with
multiple buyers and sellers and two-sided independent private information about
valuations. We show that any weighted average of revenue and social welfare can be
maximized through appropriately chosen transaction fees and that in increasingly
thin markets such optimal fees converge to linear fees. Moreover, fees decrease with
competition (or the weight on welfare) and the elasticity of supply but decrease
with the elasticity of demand. Our theoretical predictions fit empirical observations
in several industries with intermediaries
Separation of Test-Free Propositional Dynamic Logics over Context-Free Languages
For a class L of languages let PDL[L] be an extension of Propositional
Dynamic Logic which allows programs to be in a language of L rather than just
to be regular. If L contains a non-regular language, PDL[L] can express
non-regular properties, in contrast to pure PDL.
For regular, visibly pushdown and deterministic context-free languages, the
separation of the respective PDLs can be proven by automata-theoretic
techniques. However, these techniques introduce non-determinism on the automata
side. As non-determinism is also the difference between DCFL and CFL, these
techniques seem to be inappropriate to separate PDL[DCFL] from PDL[CFL].
Nevertheless, this separation is shown but for programs without test operators.Comment: In Proceedings GandALF 2011, arXiv:1106.081
Extended Computation Tree Logic
We introduce a generic extension of the popular branching-time logic CTL
which refines the temporal until and release operators with formal languages.
For instance, a language may determine the moments along a path that an until
property may be fulfilled. We consider several classes of languages leading to
logics with different expressive power and complexity, whose importance is
motivated by their use in model checking, synthesis, abstract interpretation,
etc.
We show that even with context-free languages on the until operator the logic
still allows for polynomial time model-checking despite the significant
increase in expressive power. This makes the logic a promising candidate for
applications in verification.
In addition, we analyse the complexity of satisfiability and compare the
expressive power of these logics to CTL* and extensions of PDL
History-deterministic Vector Addition Systems
We consider history-determinism, a restricted form of non-determinism, for
Vector Addition Systems with States (VASS) when used as acceptors to recognise
languages of finite words. History-determinism requires that the
non-deterministic choices can be resolved on-the-fly; based on the past and
without jeopardising acceptance of any possible continuation of the input word.
Our results show that the history-deterministic (HD) VASS sit strictly
between deterministic and non-deterministic VASS regardless of the number of
counters. We compare the relative expressiveness of HD systems, and
closure-properties of the induced language classes, with coverability and
reachability semantics, and with and without -labelled
transitions.
Whereas in dimension 1, inclusion and regularity remain decidable, from
dimension two onwards, HD-VASS with suitable resolver strategies, are
essentially able to simulate 2-counter Minsky machines, leading to several
undecidability results: It is undecidable whether a VASS is
history-deterministic, or if a language equivalent history-deterministic VASS
exists. Checking language inclusion between history-deterministic 2-VASS is
also undecidable.Comment: This is the full version of a paper published in CONCUR 202
Model Checking Probabilistic Pushdown Automata
We consider the model checking problem for probabilistic pushdown automata
(pPDA) and properties expressible in various probabilistic logics. We start
with properties that can be formulated as instances of a generalized random
walk problem. We prove that both qualitative and quantitative model checking
for this class of properties and pPDA is decidable. Then we show that model
checking for the qualitative fragment of the logic PCTL and pPDA is also
decidable. Moreover, we develop an error-tolerant model checking algorithm for
PCTL and the subclass of stateless pPDA. Finally, we consider the class of
omega-regular properties and show that both qualitative and quantitative model
checking for pPDA is decidable
Fee-Setting Mechanisms: On Optimal Pricing by Intermediaries and Indirect Taxation
Mechanisms according to which private intermediaries or governments charge
transaction fees or indirect taxes are prevalent in practice. We consider a setup with
multiple buyers and sellers and two-sided independent private information about
valuations. We show that any weighted average of revenue and social welfare can be
maximized through appropriately chosen transaction fees and that in increasingly
thin markets such optimal fees converge to linear fees. Moreover, fees decrease with
competition (or the weight on welfare) and the elasticity of supply but decrease
with the elasticity of demand. Our theoretical predictions fit empirical observations
in several industries with intermediaries
Languages Generated by Iterated Idempotencies.
The rewrite relation with parameters m and n and with the possible length limit = k or :::; k we denote by w~, =kW~· or ::;kw~ respectively. The idempotency languages generated from a starting word w by the respective operations are wDAlso other special cases of idempotency languages besides duplication have come up in different contexts. The investigations of Ito et al. about insertion and deletion, Le., operations that are also observed in DNA molecules, have established that w5 and w~ both preserve regularity.Our investigations about idempotency relations and languages start out from the case of a uniform length bound. For these relations =kW~ the conditions for confluence are characterized completely. Also the question of regularity is -k n answered for aH the languages w- D 1 are more complicated and belong to the class of context-free languages.For a generallength bound, i.e."for the relations :"::kW~, confluence does not hold so frequently. This complicatedness of the relations results also in more complicated languages, which are often non-regular, as for example the languages WWithout any length bound, idempotency relations have a very complicated structure. Over alphabets of one or two letters we still characterize the conditions for confluence. Over three or more letters, in contrast, only a few cases are solved. We determine the combinations of parameters that result in the regularity of wDIn a second chapter sorne more involved questions are solved for the special case of duplication. First we shed sorne light on the reasons why it is so difficult to determine the context-freeness ofduplication languages. We show that they fulfiH aH pumping properties and that they are very dense. Therefore aH the standard tools to prove non-context-freness do not apply here.The concept of root in Formal Language ·Theory is frequently used to describe the reduction of a word to another one, which is in sorne sense elementary.For example, there are primitive roots, periodicity roots, etc. Elementary in connection with duplication are square-free words, Le., words that do not contain any repetition. Thus we define the duplication root of w to consist of aH the square-free words, from which w can be reached via the relation w~.Besides sorne general observations we prove the decidability of the question, whether the duplication root of a language is finite.Then we devise acode, which is robust under duplication of its code words.This would keep the result of a computation from being destroyed by dupli cations in the code words. We determine the exact conditions, under which infinite such codes exist: over an alphabet of two letters they exist for a length bound of 2, over three letters already for a length bound of 1.Also we apply duplication to entire languages rather than to single words; then it is interesting to determine, whether regular and context-free languages are closed under this operation. We show that the regular languages are closed under uniformly bounded duplication, while they are not closed under duplication with a generallength bound. The context-free languages are closed under both operations.The thesis concludes with a list of open problems related with the thesis' topics
History-deterministic Vector Addition Systems
We consider history-determinism, a restricted form of non-determinism, for Vector Addition Systems with States (VASS) when used as acceptors to recognise languages of finite words. History-determinism requires that the non-deterministic choices can be resolved on-the-fly; based on the past and without jeopardising acceptance of any possible continuation of the input word.
Our results show that the history-deterministic (HD) VASS sit strictly between deterministic and non-deterministic VASS regardless of the number of counters. We compare the relative expressiveness of HD systems, and closure-properties of the induced language classes, with coverability and reachability semantics, and with and without ?-labelled transitions.
Whereas in dimension 1, inclusion and regularity remain decidable, from dimension two onwards, HD-VASS with suitable resolver strategies, are essentially able to simulate 2-counter Minsky machines, leading to several undecidability results: It is undecidable whether a VASS is history-deterministic, or if a language equivalent history-deterministic VASS exists. Checking language inclusion between history-deterministic 2-VASS is also undecidable
Resource Bisimilarity in Petri Nets is Decidable
Petri nets are a popular formalism for modeling and analyzing distributed
systems. Tokens in Petri net models can represent the control flow state or
resources produced/consumed by transition firings. We define a resource as a
part (submultiset) of the Petri net marking and call two resources equivalent
iff replacing one of them with another in any marking does not change the
observable Petri net behavior. We investigate the resource similarity and the
resource bisimilarity -- congruent restrictions of the bisimulation equivalence
on Petri net markings and prove that the resource bisimilarity is decidable in
contrast to the resource similarity.Comment: New version for submission to the journa
Adaptivity in High-Performance Embedded Systems: a Reactive Control Model for Reliable and Flexible Design
International audienceSystem adaptivity is increasingly demanded in high-performance embedded systems, particularly in multimedia System-on-Chip (SoC), due to growing Quality of Service requirements. This paper presents a reactive control model that has been introduced in Gaspard, our framework dedicated to SoC hardware/software co-design. This model aims at expressing adaptivity as well as reconfigurability in systems performing data-intensive computations. It is generic enough to be used for description in the different parts of an embedded system, e.g. specification of how different data-intensive algorithms can be chosen according to some computation modes at the functional level; expression of how hardware components can be selected via the usage of a library of Intellectual Properties (IPs) according to execution performances. The transformation of this model towards synchronous languages is also presented, in order to allow an automatic code generation usable for formal verification, based of techniques such as model checking and controller synthesis as illustrated in the paper. This work, based on Model-Driven Engineering and the standard UML MARTE profile, has been implemented in Gaspard
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