3,588 research outputs found
Regular realizability problems and context-free languages
We investigate regular realizability (RR) problems, which are the problems of
verifying whether intersection of a regular language -- the input of the
problem -- and fixed language called filter is non-empty. In this paper we
focus on the case of context-free filters. Algorithmic complexity of the RR
problem is a very coarse measure of context-free languages complexity. This
characteristic is compatible with rational dominance. We present examples of
P-complete RR problems as well as examples of RR problems in the class NL. Also
we discuss RR problems with context-free filters that might have intermediate
complexity. Possible candidates are the languages with polynomially bounded
rational indices.Comment: conference DCFS 201
Parametric Linear Dynamic Logic
We introduce Parametric Linear Dynamic Logic (PLDL), which extends Linear
Dynamic Logic (LDL) by temporal operators equipped with parameters that bound
their scope. LDL was proposed as an extension of Linear Temporal Logic (LTL)
that is able to express all -regular specifications while still
maintaining many of LTL's desirable properties like an intuitive syntax and a
translation into non-deterministic B\"uchi automata of exponential size. But
LDL lacks capabilities to express timing constraints. By adding parameterized
operators to LDL, we obtain a logic that is able to express all
-regular properties and that subsumes parameterized extensions of LTL
like Parametric LTL and PROMPT-LTL. Our main technical contribution is a
translation of PLDL formulas into non-deterministic B\"uchi word automata of
exponential size via alternating automata. This yields a PSPACE model checking
algorithm and a realizability algorithm with doubly-exponential running time.
Furthermore, we give tight upper and lower bounds on optimal parameter values
for both problems. These results show that PLDL model checking and
realizability are not harder than LTL model checking and realizability.Comment: In Proceedings GandALF 2014, arXiv:1408.556
Towards Realizability Checking of Contracts using Theories
Virtual integration techniques focus on building architectural models of
systems that can be analyzed early in the design cycle to try to lower cost,
reduce risk, and improve quality of complex embedded systems. Given appropriate
architectural descriptions and compositional reasoning rules, these techniques
can be used to prove important safety properties about the architecture prior
to system construction. Such proofs build from "leaf-level" assume/guarantee
component contracts through architectural layers towards top-level safety
properties. The proofs are built upon the premise that each leaf-level
component contract is realizable; i.e., it is possible to construct a component
such that for any input allowed by the contract assumptions, there is some
output value that the component can produce that satisfies the contract
guarantees. Without engineering support it is all too easy to write leaf-level
components that can't be realized. Realizability checking for propositional
contracts has been well-studied for many years, both for component synthesis
and checking correctness of temporal logic requirements. However, checking
realizability for contracts involving infinite theories is still an open
problem. In this paper, we describe a new approach for checking realizability
of contracts involving theories and demonstrate its usefulness on several
examples.Comment: 15 pages, to appear in NASA Formal Methods (NFM) 201
Models of Intuitionistic Set Theory in Subtoposes of Nested Realizability Toposes
With every pca and subpca we associate the
nested realizability topos within
which we identify a class of small maps giving rise to a model of
intuitionistic set theory within . For
every subtopos of such a nested realizability topos we construct
an induced class of small maps in giving rise to
a model of intuitionistic set theory within . This covers relative
realizability toposes, modified relative realizability toposes, the modified
realizability topos and van den Berg's recent Herbrand topos
Parameterized Synthesis
We study the synthesis problem for distributed architectures with a
parametric number of finite-state components. Parameterized specifications
arise naturally in a synthesis setting, but thus far it was unclear how to
detect realizability and how to perform synthesis in a parameterized setting.
Using a classical result from verification, we show that for a class of
specifications in indexed LTL\X, parameterized synthesis in token ring networks
is equivalent to distributed synthesis in a network consisting of a few copies
of a single process. Adapting a well-known result from distributed synthesis,
we show that the latter problem is undecidable. We describe a semi-decision
procedure for the parameterized synthesis problem in token rings, based on
bounded synthesis. We extend the approach to parameterized synthesis in
token-passing networks with arbitrary topologies, and show applicability on a
simple case study. Finally, we sketch a general framework for parameterized
synthesis based on cutoffs and other parameterized verification techniques.Comment: Extended version of TACAS 2012 paper, 29 page
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