Checkpoint mechanism for Z3 - z3

I am planning to do some work with the Z3 SMT solver from Microsoft Research that will run on a compute server with an execution time limit. I expect that the job will exceed this limit. The recommended policy for this computing center is to use "checkpoints" and to invoke a series of jobs, each of which picks up the checkpoint from the previous job and continues working. In this way, no process runs for more than the execution time limit, so other users have a chance to run their jobs too, but the total amount of compute time used can exceed the timeout for a single job.
Does Z3 have support for reading and writing checkpoints?
By "checkpoint", I mean a file that serializes (some part of) the internal state of the Z3 solver, such that if the Z3 process writes a checkpoint and exits, and then a second Z3 process is started that reads the checkpoint file, after reading it back the state of the new Z3 process is identical to the state of the previous process (so the solver doesn't start again, but continues solving from where it left off).
As an alternative, instead of checkpointing the entire solver, is it possible to read the database of learned clauses (or other inference databases built internally by Z3)? This could make it possible to do a form of checkpointing by augmenting the input file with learned clauses, although it might not be as efficient as a "real" checkpoint of the entire internal state.

No, Z3 does not have facilities that achieve all those goals already built in. Z3 goal and solver objects can be serialized to a string in SMT2 format via the Z3_goal_to_string and Z3_solver_to_string functions; these could be used for check-pointing, but they will not save any learnt clauses that weren't in the goal or the solver before the last search was started.
In case the main goal is to re-start an intricate interaction, perhaps a Z3 interaction log could be helpful (see Z3_open_log). These logs can be replayed, but again, learned clauses, etc, are not saved.

Related

Speculative Execution in Apache Beam

I don't see any mention of speculative execution in Apache Beam documentation. But this post claims that it has something like that.
the ParDo transformation is fault-tolerant, i.e. if it crashes, it's
rerun. The transformation also has a concept of speculative execution
(read about speculative execution in Spark, both are similar basics).
The processing for given subset of dataset can be executed on 2
different workers at any time. The results coming from the quickest
worker are later used and for the slower one are discarded. At this
occasion it's important to emphasize that ParDo implementation must be
aware of parallel execution on the same subset of data.
Is it true?
I believe that speculative execution is a responsibility of data processing engine, not Beam. Though, one of the requirement for a Beam transform is to be idempotent because Beam model provides no guarantees as to the number of times your user code might be invoked or retried (see transform requirements).
There is no similar design in beam. You can look at the documentation here [1] which has lot of details around this topic.
https://github.com/apache/beam/blob/master/sdks/java/core/src/main/java/org/apache/beam/sdk/transforms/ParDo.java#L365

How do I make sure my Dataflow pipeline scales?

We've often seen people write Dataflow pipelines that don't scale well. This is frustrating since Dataflow is meant to scale transparently, but there still are some antipatterns in Dataflow pipelines that make it difficult to scale. What are some common antipatterns and tips for avoiding them?
Scaling Your Dataflow Pipeline
Hi, Reuven Lax here. I’m a member of the Dataflow engineering team, where I lead the design and implementation of our streaming runner. Prior to Dataflow I led the team that built MillWheel for a number of years. MillWheel was described in this VLDB 2013 paper, and is the basis for the streaming technology underlying Dataflow.
Dataflow usually removes the need for you to think too much about how to make a pipeline scale. A lot of work has gone into sophisticated algorithms that can automatically parallelize and tune your pipeline across many machines. However as with any such system, there are some anti-patterns that can bottleneck your pipeline at scale. In this post we will go over three of these anti-patterns, and discuss how to address them. It’s assumed that you are already familiar with the Dataflow programming model. If not, I recommend beginning with our Getting Started guide and Tyler Akidau’s Streaming 101 and Streaming 102 blog posts. You may also read the Dataflow model paper published in VLDB 2015.
Today we’re going to talk about scaling your pipeline - or more specifically, why your pipeline might not scale. When we say scalability, we mean the ability of the pipeline to operate efficiently as input size increases and key distribution changes. The scenario: you’ve written a cool new Dataflow pipeline, which the high-level operations we provide made easy to write. You’ve tested this pipeline locally on your machine using DirectPipelineRunner and everything looks fine. You’ve even tried deploying it on a small number of Compute VMs, and things still look rosy. Then you try and scale up to a larger data volume, and the picture becomes decidedly worse. For a batch pipeline, it takes far longer than expected for the pipeline to complete. For a streaming pipeline, the lag reported in the Dataflow UI keeps increasing as the pipeline falls further and further behind. We’re going to explain some reasons this might happen, and how to address them.
Expensive Per-Record Operations
One common problem we see is pipelines that perform needlessly expensive or slow operations for each record processed. Technically this isn’t a hard scaling bottleneck - given enough resources, Dataflow can still distribute this pipeline on enough machines to make it perform well. However when running over many millions or billions of records, the cost of these per-record operations adds up to an unexpectedly-large number. Usually these problems aren’t noticeable at all at lower scale.
Here’s an example of one such operation, taken from a real Dataflow pipeline.
import javax.json.Json;
...
PCollection<OutType> output = input.apply(ParDo.of(new DoFn<InType, OutType>() {
public void processElement(ProcessContext c) {
JsonReader reader = Json.createReader();
// Perform some processing on entry.
...
}
}));
At first glance it’s not obvious that anything is wrong with this code, yet when run at scale this pipeline ran extremely slowly.
Since the actual business logic of our code shouldn't have caused a slowdown, we suspected that something was adding per-record overhead to our pipeline. To get more information on this, we had to ssh to the VMs to get actual thread profiles from workers. After a bit of digging, we found threads were often stuck in the following stack trace:
java.util.zip.ZipFile.getEntry(ZipFile.java:308)
java.util.jar.JarFile.getEntry(JarFile.java:240)
java.util.jar.JarFile.getJarEntry(JarFile.java:223)
sun.misc.URLClassPath$JarLoader.getResource(URLClassPath.java:1005)
sun.misc.URLClassPath$JarLoader.findResource(URLClassPath.java:983)
sun.misc.URLClassPath$1.next(URLClassPath.java:240)
sun.misc.URLClassPath$1.hasMoreElements(URLClassPath.java:250)
java.net.URLClassLoader$3$1.run(URLClassLoader.java:601)
java.net.URLClassLoader$3$1.run(URLClassLoader.java:599)
java.security.AccessController.doPrivileged(Native Method)
java.net.URLClassLoader$3.next(URLClassLoader.java:598)
java.net.URLClassLoader$3.hasMoreElements(URLClassLoader.java:623)
sun.misc.CompoundEnumeration.next(CompoundEnumeration.java:45)
sun.misc.CompoundEnumeration.hasMoreElements(CompoundEnumeration.java:54)
java.util.ServiceLoader$LazyIterator.hasNextService(ServiceLoader.java:354)
java.util.ServiceLoader$LazyIterator.hasNext(ServiceLoader.java:393)
java.util.ServiceLoader$1.hasNext(ServiceLoader.java:474)
javax.json.spi.JsonProvider.provider(JsonProvider.java:89)
javax.json.Json.createReader(Json.java:208)
<.....>.processElement(<filename>.java:174)
Each call to Json.createReader was searching the classpath trying to find a registered JsonProvider. As you can see from the stack trace, this involves loading and unzipping JAR files. Doing this per record on a high-scale pipeline is not likely to perform very well!
The solution here was for the user to create a static JsonReaderFactory and use that to instantiate the individual reader objects. You might be tempted to create a JsonReaderFactory per bundle of records instead, inside Dataflow’s startBundle method. However, while this will work well for a batch pipeline, in streaming mode the bundles may be very small - sometimes just a few records. As a result, we don’t recommend doing expensive work per bundle either. Even if you believe your pipeline will only be used in batch mode, you may in the future want to run it as a streaming pipeline. So future-proof your pipelines, by making sure they’ll work well in either mode!
Hot Keys
A fundamental primitive in Dataflow is GroupByKey. GroupByKey allows one to group a PCollection of key-value pairs so that all values for a specific key are grouped together to be processed as a unit. Most of Dataflow’s built-in aggregating transforms - Count, Top, Combine, etc. - use GroupByKey under the cover. You might have a hot key problem if a single worker is extremely busy (e.g. high CPU use determined by looking at the set of GCE workers for the job) while other workers are idle, yet the pipeline falls farther and farther behind.
The DoFn that processes the result of a GroupByKey is given an input type of KV<KeyType, Iterable<ValueType>>. This means that the entire set of all values for that key (within the current window if using windowing) is modeled as a single Iterable element. In particular, this means that all values for that key must be processed on the same machine, in fact on the same thread. Performance problems can occur in the presence of hot keys - when one or more keys receive data faster than can be processed on a single cpu. For example, consider the following code snippet
p.apply(Read.from(new UserWebEventSource())
.apply(new ExtractBrowserString())
.apply(Window.<Event>into(FixedWindow.of(1, Duration.standardSeconds(1))))
.apply(GroupByKey.<String, Event>create())
.apply(ParDo.of(new ProcessEventsByBrowser()));
This code keys all user events by the user’s web browser, and then processes all events for each browser as a unit. However there is a small number of very popular browsers (such as Chrome, IE, Firefox, Safari), and those keys will be very hot - possibly too hot to process on one CPU. In addition to performance, this is also a scalability bottleneck. Adding more workers to the pipeline will not help if there are four hot keys, since those keys can processed on at most four workers. You’ve structured your pipeline so that Dataflow can’t scale it up without violating the API contract.
One way to alleviate this is to structure the ProcessEventsByBrowser DoFn as a combiner. A combiner is a special type of user function that allows piecewise processing of the iterable. For example, if the goal was to count the number of events per browser per second, Count.perKey() can be used instead of a ParDo. Dataflow is able to lift part of the combining operation above the GroupByKey, which allows for more parallelism (for those of you coming from the Database world, this is similar to pushing a predicate down); some of the work can be done in a previous stage which hopefully is better distributed.
Unfortunately, while using a combiner often helps, it may not be enough - especially if the hot keys are very hot; this is especially true for streaming pipelines. You might also see this when using the global variants of combine (Combine.globally(), Count.globally(), Top.largest(), among others.). Under the covers these operations are performing a per-key combine on a single static key, and may not perform well if the volume to this key is too high. To address this we allow you to provide extra parallelism hints using the Combine.PerKey.withHotKeyFanout or Combine.Globally.withFanout. These operations will create an extra step in your pipeline to pre-aggregate the data on many machines before performing the final aggregation on the target machines. There's no magic number for these operations, but the general strategy would be to split any hot key into enough sub-shards so that any single shard is well under the per-worker throughput that your pipeline can sustain.
Large Windows
Dataflow provides a sophisticated windowing facility for bucketing data according to time. This is most useful in streaming pipelines when processing unbounded data, however, it is fully supported for batch, bounded pipelines as well. When a windowing strategy has been attached to a PCollection, any subsequent grouping operation (most notably GroupByKey) performs a separate grouping per window. Unlike other systems that provide only globally-synchronized windows, Dataflow windows the data for each key separately. This is what us to provide flexible per-key windows such as sessions. For more information, I recommend that you read the windowing guide in the Dataflow documentation.
As a consequence of the fact that windows are per key, Dataflow buffers elements on the receiver side while waiting for each window to close. If using very-long windows - e.g. a 24-hour fixed window - this means that a lot of data has to be buffered, which can be a performance bottleneck for the pipeline. This can manifest as slowness (like for hot keys), or even as out of memory errors on the workers (visible in the logs). We again recommend using combiners to reduce the data size. The difference between writing this:
pcollection.apply(Window.into(FixedWindows.of(1, TimeUnit.DAYS)))
.apply(GroupByKey.<KeyType, ValueType>create())
.apply(ParDo.of(new DoFn<KV<KeyType, Iterable<ValueType>>, Long>() {
public void processElement(ProcessContext c) {
c.output(c.element().size());
}
}));
… and this ...
pcollection.apply(Window.into(FixedWindows.of(1, TimeUnit.DAYS)))
.apply(Count.perKey());
… isn’t just brevity. In the latter snippet Dataflow knows that a count combiner is being applied, and so only needs to store the count so far for each key, no matter how long the window is. In contrast, Dataflow understands less about the first snippet of code and is forced to buffer an entire day’s worth of data on receivers, even though the two snippets are logically equivalent!
If it’s impossible to express your operation as a combiner, then we recommend looking at the triggers API. This will allow you to optimistically process portions of the window before the window closes, and so reduce the size of buffered data.
Note that many of these limitations do not apply to the batch runner. However as mentioned above, you're always better off future proofing your pipeline and making sure it runs well in both modes.
We've talked about hot keys, large windows, and expensive per-record operations. Other guidance can be found in our documentation. Although this post has focused on challenges you may encounter with scaling your pipeline, there are many benefits to Dataflow that are largely transparent -- things like dynamic work rebalancing to minimize straggler effects, throughput-based autoscaling, and job resource management adapt to many different pipeline and data shapes without user intervention. We're always trying to make our system more adaptive, and plan to automatically incorporate some of the above strategies into the core execution engine over time. Thanks for reading, and happy Dataflowing!

Z3 Command-line Timeout

When using Z3 on the command line with the "-T" switch, is there a way to set the timeout to less than one second?
I know you can set the timeout to be less than that using the API, but for various stupid reasons I've been passing text files containing SMT-LIBv2 scripts to Z3 in a loop (please don't be mad), thinking it would work just as well. I've only just noticed that this approach seems to create a lower bound of one second on timeouts. This slows things down quite a bit if I'm using Z3 to check thousands of short files.
I understand if this is just the way things are, and I accept that what I'm doing isn't sensible when there's already a perfectly good API for Z3.
There are two options:
You can use "soft timeouts". They are less reliable than the timeout /T because soft timeout expiration is only checked periodically. Nevertheless, the option "smt.soft_timeout=10" would set a timeout of 10ms (instead of 10s). You can set the these options both from the command-line and within the SMT-LIB2 file using (set-option :smt.soft_timeout 10). The tutorial on using tactics/solvers furthermore explains how to use more advanced features (strategies) and you can also control these advanced features using options, such as timeouts, from the textual interface.
You can load SMT-LIB2 files from the programmatic API. The assertions from the files are stored in a conjunction. You can then call a solver (again from the API) and use the "soft timeout" option for the solver object. There isn't really a reason to use option 2 unless you need to speed up your pipe or use something more than the soft timeout feature because it is already reasonably exposed for the SMT-LIB level.

What function is to small for spawning into an own process

Where is the limit where there is no benefit of spawning a process to make a more parallelized function call?
For example when doing a recursive lookup in a tree structure, each child node would add a process and a message call to the parent just for a simple comparison.
Spawning process and do the work will be always slower than just do the work. It strongly depend on your exact requirements. Especially non-function requirements are the key. So go and do measurements. It's pretty easy. See documentation about Profiling for more details and there are also 3rd party projects easing benchmarking over there.
Spawning more processes won't necessarily make tasks run in parallel. For example, if you have a 24 cores on your system, only 24 processes can run at any one time.
Instead it might be good to think about how much work is being done when you examine a node in a tree. Lets say the node value represents a url which needs to be called to retrieve a value. In this case it might be a good idea to spawn a process for each node. This way a process can be scheduled to run while another process is waiting for an answer to the http request.

Process balancing in Erlang

Does anybody knows if there is a sort of 'load-balancer' in the erlang standard library? I mean, if I have some really simple operations on a really large set of data, the overhead of constructing a process for every item will be larger than perform the operation sequentially. But if I can balance the work in the 'right number' of process, it will perform better, so I'm basically asking if there is an easy way to accomplish this task.
By the way, does anybody knows if an OTP application does some kind of balance load? I mean, in an OTP application there is the concept of a "worker process" (like a java-ish thread worker)?
See modules pg2 and pool.
pg2 implements quite simple distributed process pool. pg2:get_closest_pid/1 returns "closest" pid, i.e. random local process if available, otherwise random remote process.
pool implements load balancing between nodes started with module slave.
The plists module probably does what you want. It is basically a parallel implementation of the lists module, design to be used as a drop-in replacement. However, you can also control how it parallelizes its operations, for example by defining how many worker processes should be spawned etc.
You probably would do it by calculating some number of workers depending on the length of the list or the load of the system etc.
From the website:
plists is a drop-in replacement for
the Erlang module lists, making most
list operations parallel. It can
operate on each element in parallel,
for IO-bound operations, on sublists
in parallel, for taking advantage of
multi-core machines with CPU-bound
operations, and across erlang nodes,
for parallizing inside a cluster. It
handles errors and node failures. It
can be configured, tuned, and tweaked
to get optimal performance while
minimizing overhead.
There is no, in my view, usefull generic load-balancing tool in otp. And perhaps it only usefull to have one in specific cases. It is easy enough to implement one yourself. plists may be useful in the same cases. I do not believe in parallel-libraries as a substitute to the real thing. Amdahl will haunt you forever if you walk this path.
The right number of worker processes is equal to the number of schedulers. This may vary depending of what other work is done on the system. Use,
erlang:system_info(schedulers_online) -> NS
to get the number of schedulers.
The notion of overhead when flooding the system with an abundance of worker processes is somewhat faulty. There is overhead with new processes but not as much as with os-threads. The main overhead is message copying between processes, this can be alleviated with the use of binaries since only the reference to the binary is sent. With eterms the structure is first expanded then copied to the other process.
There is no way how to predict cost of work mechanically without measure it e.g do it. Some person must determine how to partition work for some class of tasks. In load balancer word I understand something very different than in your question.

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