Learning commutative deterministic finite state automata in polynomial time

1991 ◽  
Vol 8 (4) ◽  
pp. 319-335 ◽  
Author(s):  
Naoki Abe
Keyword(s):  
Polynomial Time ◽  
Finite State Automata ◽  
Finite State

scholarly journals Copyful Streaming String Transducers

2021 ◽  
Vol 178 (1-2) ◽  
pp. 59-76
Author(s):  
Emmanuel Filiot ◽  
Pierre-Alain Reynier
Keyword(s):  
Polynomial Time ◽  
Equivalence Problem ◽  
Expressive Power ◽  
The Other ◽  
Finite State Automata ◽  
Finite State ◽  
Variable Content ◽  
Deterministic Automata ◽  
Intermediate Output ◽  
Linear Manner

Copyless streaming string transducers (copyless SST) have been introduced by R. Alur and P. Černý in 2010 as a one-way deterministic automata model to define transductions of finite strings. Copyless SST extend deterministic finite state automata with a set of variables in which to store intermediate output strings, and those variables can be combined and updated all along the run, in a linear manner, i.e., no variable content can be copied on transitions. It is known that copyless SST capture exactly the class of MSO-definable string-to-string transductions, and are as expressive as deterministic two-way transducers. They enjoy good algorithmic properties. Most notably, they have decidable equivalence problem (in PSpace). On the other hand, HDT0L systems have been introduced for a while, the most prominent result being the decidability of the equivalence problem. In this paper, we propose a semantics of HDT0L systems in terms of transductions, and use it to study the class of deterministic copyful SST. Our contributions are as follows: (i)HDT0L systems and total deterministic copyful SST have the same expressive power, (ii)the equivalence problem for deterministic copyful SST and the equivalence problem for HDT0L systems are inter-reducible, in quadratic time. As a consequence, equivalence of deterministic SST is decidable, (iii)the functionality of non-deterministic copyful SST is decidable, (iv)determining whether a non-deterministic copyful SST can be transformed into an equivalent non-deterministic copyless SST is decidable in polynomial time.

scholarly journals Model checking usage policies

2014 ◽  
Vol 25 (3) ◽  
pp. 710-763 ◽  
Author(s):  
MASSIMO BARTOLETTI ◽  
PIERPAOLO DEGANO ◽  
GIAN LUIGI FERRARI ◽  
ROBERTO ZUNINO
Keyword(s):  
Model Checking ◽  
Polynomial Time ◽  
Real World ◽  
Formal Model ◽  
Expressive Power ◽  
Finite State Automata ◽  
Time Model ◽  
Real World Applications ◽  
Finite State ◽  
Resource Creation

We study usage automata, a formal model for specifying policies on the usage of resources. Usage automata extend finite state automata with some additional features, parameters and guards, that improve their expressivity. We show that usage automata are expressive enough to model policies of real-world applications. We discuss their expressive power, and we prove that the problem of telling whether a computation complies with a usage policy is decidable. The main contribution of this paper is a model checking technique for usage automata. The model is that of usages, i.e. basic processes that describe the possible patterns of resource access and creation. In spite of the model having infinite states, because of recursion and resource creation, we devise a polynomial-time model checking technique for deciding when a usage complies with a usage policy.

scholarly journals The conjugacy problem for Higman’s group

2020 ◽  
Vol 30 (06) ◽  
pp. 1211-1235
Author(s):  
Owen Baker
Keyword(s):  
Fixed Points ◽  
Polynomial Time ◽  
Conjugacy Problem ◽  
Simple Groups ◽  
Finite State Automata ◽  
Dehn Function ◽  
Power Circuit ◽  
Finite State Transducers ◽  
Finite State ◽  
Circuit Technology

Higman’s group [Formula: see text] is a remarkable group with large (non-elementary) Dehn function. Higman constructed the group in 1951 to produce the first examples of infinite simple groups. Using finite state automata, and studying fixed points of certain finite state transducers, we show the conjugacy problem in [Formula: see text] is decidable for all inputs. Diekert, Laun and Ushakov have recently shown the word problem in [Formula: see text] is solvable in polynomial time, using the power circuit technology of Myasnikov, Ushakov and Won. Building on this work, we also show in a strongly generic setting that the conjugacy problem for [Formula: see text] has a polynomial time solution.

A Time Complexity Gap for Two-Way Probabilistic Finite-State Automata

1990 ◽  
Vol 19 (6) ◽  
pp. 1011-1023 ◽  
Author(s):  
Cynthia Dwork ◽  
Larry Stockmeyer
Keyword(s):  
Time Complexity ◽  
Finite State Automata ◽  
Finite State ◽  
Probabilistic Finite State Automata

Characterizations of rough finite state automata

2015 ◽  
Vol 8 (3) ◽  
pp. 721-730 ◽  
Author(s):  
Shambhu Sharan ◽  
Arun K. Srivastava ◽  
S. P. Tiwari
Keyword(s):  
Finite State Automata ◽  
Finite State

Synthesis with Mandatory Stop Actions

2021 ◽  
Author(s):  
Giuseppe De Giacomo ◽  
Antonio Di Stasio ◽  
Giuseppe Perelli ◽  
Shufang Zhu
Keyword(s):  
Model Checking ◽  
Finite State Automata ◽  
Deep Impact ◽  
Synthesis Technique ◽  
Büchi Automata ◽  
Finite State ◽  
Ltl Synthesis ◽  
Buchi Automata ◽  
The Impact

We study the impact of the need for the agent to obligatorily instruct the action stop in her strategies. More specifically we consider synthesis (i.e., planning) for LTLf goals under LTL environment specifications in the case the agent must mandatorily stop at a certain point. We show that this obligation makes it impossible to exploit the liveness part of the LTL environment specifications to achieve her goal, effectively reducing the environment specifications to their safety part only. This has a deep impact on the efficiency of solving the synthesis, which can sidestep handling Buchi determinization associated to LTL synthesis, in favor of finite-state automata manipulation as in LTLf synthesis. Next, we add to the agent goal, expressed in LTLf, a safety goal, expressed in LTL. Safety goals must hold forever, even when the agent stops, since the environment can still continue its evolution. Hence the agent, before stopping, must ensure that her safety goal will be maintained even after she stops. To do synthesis in this case, we devise an effective approach that mixes a synthesis technique based on finite-state automata (as in the case of LTLf goals) and model-checking of nondeterministic Buchi automata. In this way, again, we sidestep Buchi automata determinization, hence getting a synthesis technique that is intrinsically simpler than standard LTL synthesis.

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