1,645 research outputs found
Trees over Infinite Structures and Path Logics with Synchronization
We provide decidability and undecidability results on the model-checking
problem for infinite tree structures. These tree structures are built from
sequences of elements of infinite relational structures. More precisely, we
deal with the tree iteration of a relational structure M in the sense of
Shelah-Stupp. In contrast to classical results where model-checking is shown
decidable for MSO-logic, we show decidability of the tree model-checking
problem for logics that allow only path quantifiers and chain quantifiers
(where chains are subsets of paths), as they appear in branching time logics;
however, at the same time the tree is enriched by the equal-level relation
(which holds between vertices u, v if they are on the same tree level). We
separate cleanly the tree logic from the logic used for expressing properties
of the underlying structure M. We illustrate the scope of the decidability
results by showing that two slight extensions of the framework lead to
undecidability. In particular, this applies to the (stronger) tree iteration in
the sense of Muchnik-Walukiewicz.Comment: In Proceedings INFINITY 2011, arXiv:1111.267
Adaptable processes
We propose the concept of adaptable processes as a way of overcoming the
limitations that process calculi have for describing patterns of dynamic
process evolution. Such patterns rely on direct ways of controlling the
behavior and location of running processes, and so they are at the heart of the
adaptation capabilities present in many modern concurrent systems. Adaptable
processes have a location and are sensible to actions of dynamic update at
runtime; this allows to express a wide range of evolvability patterns for
concurrent processes. We introduce a core calculus of adaptable processes and
propose two verification problems for them: bounded and eventual adaptation.
While the former ensures that the number of consecutive erroneous states that
can be traversed during a computation is bound by some given number k, the
latter ensures that if the system enters into a state with errors then a state
without errors will be eventually reached. We study the (un)decidability of
these two problems in several variants of the calculus, which result from
considering dynamic and static topologies of adaptable processes as well as
different evolvability patterns. Rather than a specification language, our
calculus intends to be a basis for investigating the fundamental properties of
evolvable processes and for developing richer languages with evolvability
capabilities
Interval-based Synthesis
We introduce the synthesis problem for Halpern and Shoham's modal logic of
intervals extended with an equivalence relation over time points, abbreviated
HSeq. In analogy to the case of monadic second-order logic of one successor,
the considered synthesis problem receives as input an HSeq formula phi and a
finite set Sigma of propositional variables and temporal requests, and it
establishes whether or not, for all possible evaluations of elements in Sigma
in every interval structure, there exists an evaluation of the remaining
propositional variables and temporal requests such that the resulting structure
is a model for phi. We focus our attention on decidability of the synthesis
problem for some meaningful fragments of HSeq, whose modalities are drawn from
the set A (meets), Abar (met by), B (begins), Bbar (begun by), interpreted over
finite linear orders and natural numbers. We prove that the fragment ABBbareq
is decidable (non-primitive recursive hard), while the fragment AAbarBBbar
turns out to be undecidable. In addition, we show that even the synthesis
problem for ABBbar becomes undecidable if we replace finite linear orders by
natural numbers.Comment: In Proceedings GandALF 2014, arXiv:1408.556
Bounded Languages Meet Cellular Automata with Sparse Communication
Cellular automata are one-dimensional arrays of interconnected interacting
finite automata. We investigate one of the weakest classes, the real-time
one-way cellular automata, and impose an additional restriction on their
inter-cell communication by bounding the number of allowed uses of the links
between cells. Moreover, we consider the devices as acceptors for bounded
languages in order to explore the borderline at which non-trivial decidability
problems of cellular automata classes become decidable. It is shown that even
devices with drastically reduced communication, that is, each two neighboring
cells may communicate only constantly often, accept bounded languages that are
not semilinear. If the number of communications is at least logarithmic in the
length of the input, several problems are undecidable. The same result is
obtained for classes where the total number of communications during a
computation is linearly bounded
Decision Problems for Deterministic Pushdown Automata on Infinite Words
The article surveys some decidability results for DPDAs on infinite words
(omega-DPDA). We summarize some recent results on the decidability of the
regularity and the equivalence problem for the class of weak omega-DPDAs.
Furthermore, we present some new results on the parity index problem for
omega-DPDAs. For the specification of a parity condition, the states of the
omega-DPDA are assigned priorities (natural numbers), and a run is accepting if
the highest priority that appears infinitely often during a run is even. The
basic simplification question asks whether one can determine the minimal number
of priorities that are needed to accept the language of a given omega-DPDA. We
provide some decidability results on variations of this question for some
classes of omega-DPDAs.Comment: In Proceedings AFL 2014, arXiv:1405.527
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