713 research outputs found
Subsequence Automata with Default Transitions
Let be a string of length with characters from an alphabet of size
. The \emph{subsequence automaton} of (often called the
\emph{directed acyclic subsequence graph}) is the minimal deterministic finite
automaton accepting all subsequences of . A straightforward construction
shows that the size (number of states and transitions) of the subsequence
automaton is and that this bound is asymptotically optimal.
In this paper, we consider subsequence automata with \emph{default
transitions}, that is, special transitions to be taken only if none of the
regular transitions match the current character, and which do not consume the
current character. We show that with default transitions, much smaller
subsequence automata are possible, and provide a full trade-off between the
size of the automaton and the \emph{delay}, i.e., the maximum number of
consecutive default transitions followed before consuming a character.
Specifically, given any integer parameter , , we
present a subsequence automaton with default transitions of size
and delay . Hence, with we
obtain an automaton of size and delay . On
the other extreme, with , we obtain an automaton of size and delay , thus matching the bound for the standard subsequence
automaton construction. Finally, we generalize the result to multiple strings.
The key component of our result is a novel hierarchical automata construction
of independent interest.Comment: Corrected typo
Reachability for dynamic parametric processes
In a dynamic parametric process every subprocess may spawn arbitrarily many,
identical child processes, that may communicate either over global variables,
or over local variables that are shared with their parent.
We show that reachability for dynamic parametric processes is decidable under
mild assumptions. These assumptions are e.g. met if individual processes are
realized by pushdown systems, or even higher-order pushdown systems. We also
provide algorithms for subclasses of pushdown dynamic parametric processes,
with complexity ranging between NP and DEXPTIME.Comment: 31 page
Learning Concise Models from Long Execution Traces
Abstract models of system-level behaviour have applications in design
exploration, analysis, testing and verification. We describe a new algorithm
for automatically extracting useful models, as automata, from execution traces
of a HW/SW system driven by software exercising a use-case of interest. Our
algorithm leverages modern program synthesis techniques to generate predicates
on automaton edges, succinctly describing system behaviour. It employs trace
segmentation to tackle complexity for long traces. We learn concise models
capturing transaction-level, system-wide behaviour--experimentally
demonstrating the approach using traces from a variety of sources, including
the x86 QEMU virtual platform and the Real-Time Linux kernel
Simplifying Contract-Violating Traces
Contract conformance is hard to determine statically, prior to the deployment
of large pieces of software. A scalable alternative is to monitor for contract
violations post-deployment: once a violation is detected, the trace
characterising the offending execution is analysed to pinpoint the source of
the offence. A major drawback with this technique is that, often, contract
violations take time to surface, resulting in long traces that are hard to
analyse. This paper proposes a methodology together with an accompanying tool
for simplifying traces and assisting contract-violation debugging.Comment: In Proceedings FLACOS 2012, arXiv:1209.169
Model Checking Paxos in Spin
We present a formal model of a distributed consensus algorithm in the
executable specification language Promela extended with a new type of guards,
called counting guards, needed to implement transitions that depend on majority
voting. Our formalization exploits abstractions that follow from reduction
theorems applied to the specific case-study. We apply the model checker Spin to
automatically validate finite instances of the model and to extract
preconditions on the size of quorums used in the election phases of the
protocol.Comment: In Proceedings GandALF 2014, arXiv:1408.556
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