140 research outputs found
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Reachability in Continuous Pushdown VASS
Pushdown Vector Addition Systems with States (PVASS) consist of finitely many
control states, a pushdown stack, and a set of counters that can be incremented
and decremented, but not tested for zero. Whether the reachability problem is
decidable for PVASS is a long-standing open problem.
We consider continuous PVASS, which are PVASS with a continuous semantics.
This means, the counter values are rational numbers and whenever a vector is
added to the current counter values, this vector is first scaled with an
arbitrarily chosen rational factor between zero and one. We show that
reachability in continuous PVASS is NEXPTIME-complete. Our result is unusually
robust: Reachability can be decided in NEXPTIME even if all numbers are
specified in binary. On the other hand, NEXPTIME-hardness already holds for
coverability, in fixed dimension, for bounded stack, and even if all numbers
are specified in unary
The -Complexity Of Visibly Pushdown Languages
We study the question of which visibly pushdown languages (VPLs) are in the
complexity class and how to effectively decide this question.
Our contribution is to introduce a particular subclass of one-turn VPLs, called
intermediate VPLs, for which the raised question is entirely unclear: to the
best of our knowledge our research community is unaware of containment or
non-containment in for any intermediate VPL.
Our main result states that there is an algorithm that, given a visibly
pushdown automaton, correctly outputs either that its language is in
, outputs some such that is
constant-depth reducible to (implying that is not in ),
or outputs a finite disjoint union of intermediate VPLs that is
constant-depth equivalent to. In the latter case one can moreover effectively
compute with such that the concrete
intermediate VPL is constant-depth reducible to the language . Due to their
particular nature we conjecture that either all intermediate VPLs are in
or all are not. As a corollary of our main result we obtain
that in case the input language is a visibly counter language our algorithm can
effectively determine if it is in -- hence our main result
generalizes a result by Krebs et al. stating that it is decidable if a given
visibly counter language is in (when restricted to well-matched
words).
For our proofs we revisit so-called Ext-algebras (introduced by Czarnetzki et
al.), which are closely related to forest algebras (introduced by Boja\'nczyk
and Walukiewicz), and use Green's relations.Comment: 81 page
What does this notation mean anyway? Interpreting BNF-style notation as it is used in practice
BNF (Backus Naur Form) notation, as introduced in the Algol 60 report, was followed
by numerous notational variants (EBNF ISO (1996), ABNF Crocker et al. (2008), etc.),
and later by a new metalanguage which is used for discussing structured objects in Computer Science and Mathematical Logic. We call this latter offspring of BNF MBNF
(Math BNF). MBNF is sometimes called âabstract syntaxâ. MBNF can express structured objects that cannot be serialised as finite strings. What MBNF and other BNF
variants share is the use of production rules, whose form is given below, which state
that âevery instance of âŠi
for i â {1, . . . , n} is also an instance of âąâ.
âą ::= âŠ1 | · · · | âŠn
This thesis studies BNF and its variant forms and contrasts them with MBNF production rules. We show via a series of detailed examples and lemmas that MBNF, differs
substantially from BNF and its variants in how it is written, the operations it allows,
and the sets of entities it defines. We demonstrate with an example and a proof that
MBNF has features that, when combined, could make MBNF rule sets inconsistent.
Readers do not have a document which tells them how to read MBNF and have to learn
MBNF through a process of cultural initiation. We propose a framework, MathSyn,
that handles most uses of MBNF one might encounter in the wild
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 25th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2022, which was held during April 4-6, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 23 regular papers presented in this volume were carefully reviewed and selected from 77 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems
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