1,842 research outputs found
The complexity of equivalence problems for commutative grammars
In this paper we investigate the computational complexity of the inequivalence problems for commutative grammars. We show that the inequivalence problems for type 0 and context-sensitive commutative grammars are undecidable whereas decidability in nondeterministic exponential-time holds for the classes of regular and context-free commutative grammars. For the latter the inequivalence problems are Σp2-hard
Tightening the Complexity of Equivalence Problems for Commutative Grammars
We show that the language equivalence problem for regular and context-free
commutative grammars is coNEXP-complete. In addition, our lower bound
immediately yields further coNEXP-completeness results for equivalence problems
for communication-free Petri nets and reversal-bounded counter automata.
Moreover, we improve both lower and upper bounds for language equivalence for
exponent-sensitive commutative grammars.Comment: 21 page
Complexity of Problems of Commutative Grammars
We consider commutative regular and context-free grammars, or, in other
words, Parikh images of regular and context-free languages. By using linear
algebra and a branching analog of the classic Euler theorem, we show that,
under an assumption that the terminal alphabet is fixed, the membership problem
for regular grammars (given v in binary and a regular commutative grammar G,
does G generate v?) is P, and that the equivalence problem for context free
grammars (do G_1 and G_2 generate the same language?) is in
Integer Vector Addition Systems with States
This paper studies reachability, coverability and inclusion problems for
Integer Vector Addition Systems with States (ZVASS) and extensions and
restrictions thereof. A ZVASS comprises a finite-state controller with a finite
number of counters ranging over the integers. Although it is folklore that
reachability in ZVASS is NP-complete, it turns out that despite their
naturalness, from a complexity point of view this class has received little
attention in the literature. We fill this gap by providing an in-depth analysis
of the computational complexity of the aforementioned decision problems. Most
interestingly, it turns out that while the addition of reset operations to
ordinary VASS leads to undecidability and Ackermann-hardness of reachability
and coverability, respectively, they can be added to ZVASS while retaining
NP-completness of both coverability and reachability.Comment: 17 pages, 2 figure
Safety verification of asynchronous pushdown systems with shaped stacks
In this paper, we study the program-point reachability problem of concurrent
pushdown systems that communicate via unbounded and unordered message buffers.
Our goal is to relax the common restriction that messages can only be retrieved
by a pushdown process when its stack is empty. We use the notion of partially
commutative context-free grammars to describe a new class of asynchronously
communicating pushdown systems with a mild shape constraint on the stacks for
which the program-point coverability problem remains decidable. Stacks that fit
the shape constraint may reach arbitrary heights; further a process may execute
any communication action (be it process creation, message send or retrieval)
whether or not its stack is empty. This class extends previous computational
models studied in the context of asynchronous programs, and enables the safety
verification of a large class of message passing programs
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